{"id":49,"date":"2026-08-14T19:09:16","date_gmt":"2026-08-14T19:09:16","guid":{"rendered":"https:\/\/1stmaster.com\/education\/?p=49"},"modified":"2026-08-16T20:13:28","modified_gmt":"2026-08-16T20:13:28","slug":"volume-and-surface-area-class-10-question-with-answer","status":"publish","type":"post","link":"https:\/\/1stmaster.com\/education\/volume-and-surface-area-class-10-question-with-answer\/","title":{"rendered":"Volume and Surface Area Class 10 Question PYQ"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The volume and surface area are the important chapter of CBSE Board of Class 10. We are picking up most important question with solution and we also covered PYQ questions for that chapter so that our students can make such questions and get well in the examination.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/surface-area-and-volume-class-10-1024x683.png\" alt=\"surface area and volume class 10\" class=\"wp-image-73\" srcset=\"https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/surface-area-and-volume-class-10-1024x683.png 1024w, https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/surface-area-and-volume-class-10-300x200.png 300w, https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/surface-area-and-volume-class-10-768x512.png 768w, https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/surface-area-and-volume-class-10.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-1\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area and volume of the toy. Take <math><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\pi=\\frac{22}{7}<\/annotation><\/semantics><\/math>.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-1\" hidden>Show More<\/button><\/section>\n\n\n<details class=\"accrd-accordion\"><summary class=\"accrd-summary\"><span class=\"accrd-summary-text\">Answer<\/span><span class=\"accrd-icon\" aria-hidden=\"true\"><\/span><\/summary><div class=\"accrd-body\">\n\n\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A toy is made of a cone mounted on a hemisphere.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Radius <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mn>3.5<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">r=3.5\\text{ cm}<\/annotation><\/semantics><\/math>r=3.5\u00a0cm<\/li>\n\n\n\n<li>Total height = 15.5 cm<\/li>\n\n\n\n<li><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\pi=\\frac{22}{7}<\/annotation><\/semantics><\/math>\u03c0=722\u200b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Height of the cone<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>15.5<\/mn><mo>\u2212<\/mo><mn>3.5<\/mn><mo>=<\/mo><mn>12<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">h=15.5-3.5=12\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Slant height of the cone<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><msqrt><mrow><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>h<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><msqrt><mrow><msup><mn>3.5<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>12<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>12.5<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">l=\\sqrt{r^2+h^2}=\\sqrt{3.5^2+12^2}=12.5\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Total Surface Area (TSA)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">TSA = Curved surface area of hemisphere + Curved surface area of cone<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>\u03c0<\/mi><mi>r<\/mi><mi>l<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">=2\\pi r^2+\\pi rl<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>3.5<\/mn><mo>\u00d7<\/mo><mn>3.5<\/mn><mo>+<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>3.5<\/mn><mo>\u00d7<\/mo><mn>12.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=2\\times\\frac{22}{7}\\times3.5\\times3.5+\\frac{22}{7}\\times3.5\\times12.5<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>77<\/mn><mo>+<\/mo><mn>137.5<\/mn><mo>=<\/mo><mn>214.5<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=77+137.5=214.5\\text{ cm}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>The TSA of toy is 214.5 cm\u00b2<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Volume of the toy<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Volume = Volume of hemisphere + Volume of cone<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{2}{3}\\pi r^3+\\frac{1}{3}\\pi r^2h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>3.5<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>3.5<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{2}{3}\\times\\frac{22}{7}\\times3.5^3+\\frac{1}{3}\\times\\frac{22}{7}\\times3.5^2\\times12<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>89.83<\/mn><mo>+<\/mo><mn>154<\/mn><mo>=<\/mo><mn>243.83<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=89.83+154=243.83\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: 243.83 cm\u00b3 (approximately 243.8 cm\u00b3)<\/p>\n\n\n\n<\/div><\/details>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-2\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-2\" hidden>Show More<\/button><\/section>\n\n\n<details class=\"accrd-accordion\"><summary class=\"accrd-summary\"><span class=\"accrd-summary-text\">Answer<\/span><span class=\"accrd-icon\" aria-hidden=\"true\"><\/span><\/summary><div class=\"accrd-body\">\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the height of the cone<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Radius = 5 cm<\/li>\n\n\n\n<li>Height of cylinder = 13 cm<\/li>\n\n\n\n<li>Height of hemisphere = 5 cm<\/li>\n\n\n\n<li>Total height = 30 cm<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>30<\/mn><mo>\u2212<\/mo><mn>13<\/mn><mo>\u2212<\/mo><mn>5<\/mn><mo>=<\/mo><mn>12<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">h=30-13-5=12\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the slant height of the cone<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><msqrt><mrow><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>h<\/mi><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><msqrt><mrow><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>12<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>13<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">l=\\sqrt{r^2+h^2}=\\sqrt{5^2+12^2}=13\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Total Surface Area<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Only the curved surfaces are calculated.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>TSA<\/mtext><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><mi>r<\/mi><mi>h<\/mi><mo>+<\/mo><mi>\u03c0<\/mi><mi>r<\/mi><mi>l<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\text{TSA}=2\\pi r^2+2\\pi rh+\\pi rl<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute the values:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>13<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>13<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">=2\\pi(5)^2+2\\pi(5)(13)+\\pi(5)(13)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>50<\/mn><mi>\u03c0<\/mi><mo>+<\/mo><mn>130<\/mn><mi>\u03c0<\/mi><mo>+<\/mo><mn>65<\/mn><mi>\u03c0<\/mi><mo>=<\/mo><mn>245<\/mn><mi>\u03c0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">=50\\pi+130\\pi+65\\pi=245\\pi<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\pi=\\frac{22}{7}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>245<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>=<\/mo><mn>770<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">245\\times\\frac{22}{7}=770\\text{ cm}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total Surface Area = 770 cm\u00b2<\/p>\n\n\n\n<\/div><\/details>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-3\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">An iron pillar has some part in the form of a right circular cylinder and the remaining part in the form of a right circular cone. The radius of the base of each of the cone and the cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if 1 cm\u00b3 of iron weighs 7.5 grams.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-3\" hidden>Show More<\/button><\/section>\n\n\n<details class=\"accrd-accordion\"><summary class=\"accrd-summary\"><span class=\"accrd-summary-text\">Answer<\/span><span class=\"accrd-icon\" aria-hidden=\"true\"><\/span><\/summary><div class=\"accrd-body\">\n\n\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Quantity<\/th><th>Value<\/th><\/tr><tr><td>Radius (r)<\/td><td>8 cm<\/td><\/tr><tr><td>Height of cylinder<\/td><td>240 cm<\/td><\/tr><tr><td>Height of cone<\/td><td>36 cm<\/td><\/tr><tr><td>Weight of 1 cm\u00b3 iron<\/td><td>7.5 g<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Volume of the pillar<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>H<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V=\\pi r^2h+\\frac13\\pi r^2H<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>8<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>240<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>8<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{22}{7}\\times8^2\\times240+\\frac13\\times\\frac{22}{7}\\times8^2\\times36<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>50688<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=50688\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Weight of the pillar<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Weight<\/mtext><mo>=<\/mo><mn>50688<\/mn><mo>\u00d7<\/mo><mn>7.5<\/mn><mo>=<\/mo><mn>380160<\/mn><mtext>\u00a0g<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Weight}=50688\\times7.5=380160\\text{ g}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Convert into kilograms:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>380160<\/mn><mn>1000<\/mn><\/mfrac><mo>=<\/mo><mn>380.16<\/mn><mtext>\u00a0kg<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{380160}{1000}=380.16\\text{ kg}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Weight of the iron pillar = 380.16 kg<\/p>\n\n\n\n<\/div><\/details>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-4\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A gulabjamun, when ready for eating, contains sugar syrup of about 30% of its volume. Find approximately, how much syrup would be found in 45 such gulabjamuns, each shaped like a cylinder with two hemispherical ends, if the complete length of each of them is 5 cm and its diameter is 2.8 cm.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-4\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-5\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total length = 5 cm<\/li>\n\n\n\n<li>Diameter = 2.8 cm \u21d2 Radius = 1.4 cm<\/li>\n\n\n\n<li>45 gulabjamuns<\/li>\n\n\n\n<li>Syrup = 30% of volume<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Height of cylindrical part<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>5<\/mn><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>1.4<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>2.2<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">h=5-2(1.4)=2.2\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Volume of one gulabjamun<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It consists of a cylinder and two hemispheres (= one sphere).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><mo>+<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\pi r^2h+\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using <math><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mn>1.4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">r=1.4<\/annotation><\/semantics><\/math>r=1.4 and <math><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>2.2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">h=2.2<\/annotation><\/semantics><\/math>h=2.2:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mn>1.4<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo stretchy=\"false\">(<\/mo><mn>2.2<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo stretchy=\"false\">(<\/mo><mn>1.4<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{22}{7}(1.4)^2(2.2)+\\frac{4}{3}\\times\\frac{22}{7}(1.4)^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mn>13.55<\/mn><mo>+<\/mo><mn>11.50<\/mn><mo>=<\/mo><mn>25.05<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=13.55+11.50=25.05\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Syrup in 45 gulabjamuns<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>30<\/mn><mi mathvariant=\"normal\">%<\/mi><mo>\u00d7<\/mo><mn>45<\/mn><mo>\u00d7<\/mo><mn>25.05<\/mn><mo>=<\/mo><mn>338.2<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">30\\%\\times45\\times25.05=338.2\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: 338 cm\u00b3 (approximately)<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-5\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-6\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A toy is in the form of a cone mounted on a hemisphere of diameter 7 cm. The total height of the toy is 14.5 cm. Find the volume and the total surface area of the toy.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-6\" hidden>Show More<\/button><\/section>\n\n\n<details class=\"accrd-accordion\"><summary class=\"accrd-summary\"><span class=\"accrd-summary-text\">Answer<\/span><span class=\"accrd-icon\" aria-hidden=\"true\"><\/span><\/summary><div class=\"accrd-body\">\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Diameter = 7 cm \u21d2 Radius = 3.5 cm<\/li>\n\n\n\n<li>Total height = 14.5 cm<\/li>\n\n\n\n<li>Cone height = 14.5 \u2212 3.5 = 11 cm<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Volume<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><mo>+<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac13\\pi r^2h+\\frac23\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>3.5<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>11<\/mn><mo>+<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>3.5<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac13\\times\\frac{22}{7}\\times3.5^2\\times11+\\frac23\\times\\frac{22}{7}\\times3.5^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>141.17<\/mn><mo>+<\/mo><mn>89.83<\/mn><mo>=<\/mo><mn>231<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=141.17+89.83=231\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Total Surface Area<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Slant height:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><msqrt><mrow><msup><mn>11<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>3.5<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>11.54<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">l=\\sqrt{11^2+3.5^2}=11.54\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>T<\/mi><mi>S<\/mi><mi>A<\/mi><mo>=<\/mo><mi>\u03c0<\/mi><mi>r<\/mi><mi>l<\/mi><mo>+<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">TSA=\\pi rl+2\\pi r^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>3.5<\/mn><mo>\u00d7<\/mo><mn>11.54<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>3.5<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{22}{7}\\times3.5\\times11.54+2\\times\\frac{22}{7}\\times3.5^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>126.94<\/mn><mo>+<\/mo><mn>77<\/mn><mo>=<\/mo><mn>203.94<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=126.94+77=203.94\\text{ cm}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume = 231 cm\u00b3<\/li>\n\n\n\n<li>Total Surface Area = 204 cm\u00b2 (approx.)<\/li>\n<\/ul>\n\n\n\n<\/div><\/details>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-7\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 98 cm and the diameter of each of its hemispherical ends is 28 cm, find the cost of polishing the surface of the solid at the rate of 15 paise per sq cm. Use <math><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\pi=\\frac{22}{7}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-7\" hidden>Show More<\/button><\/section>\n\n\n<details class=\"accrd-accordion\"><summary class=\"accrd-summary\"><span class=\"accrd-summary-text\">Answer<\/span><span class=\"accrd-icon\" aria-hidden=\"true\"><\/span><\/summary><div class=\"accrd-body\">\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total length = 98 cm<\/li>\n\n\n\n<li>Diameter = 28 cm \u21d2 Radius = 14 cm<\/li>\n\n\n\n<li>Cylinder height = 98 \u2212 28 = 70 cm<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Surface Area<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>C<\/mi><mi>S<\/mi><msub><mi>A<\/mi><mrow><mi>c<\/mi><mi>y<\/mi><mi>l<\/mi><\/mrow><\/msub><mo>=<\/mo><mn>2<\/mn><mi>\u03c0<\/mi><mi>r<\/mi><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">CSA_{cyl}=2\\pi rh<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>14<\/mn><mo>\u00d7<\/mo><mn>70<\/mn><mo>=<\/mo><mn>6160<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=2\\times\\frac{22}{7}\\times14\\times70=6160\\text{ cm}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area of two hemispheres = Area of one sphere<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>14<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>2464<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">4\\pi r^2=4\\times\\frac{22}{7}\\times14^2=2464\\text{ cm}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>T<\/mi><mi>S<\/mi><mi>A<\/mi><mo>=<\/mo><mn>6160<\/mn><mo>+<\/mo><mn>2464<\/mn><mo>=<\/mo><mn>8624<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">TSA=6160+2464=8624\\text{ cm}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Cost<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Convert paisa to ruppes we know that 1 Paisa = \u20b90.01<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">15 paise = \u20b90.15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>8624<\/mn><mo>\u00d7<\/mo><mn>0.15<\/mn><mo>=<\/mo><mn>1293.60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">8624\\times0.15=1293.60<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: \u20b91,293.60<\/p>\n\n\n\n<\/div><\/details>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-8\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. Take \u03c0 = 3.14.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-8\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-9\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cylinder: Radius = 6 cm, Height = 8 cm<\/li>\n\n\n\n<li>Conical cavity: Radius = 6 cm, Height = 8 cm<\/li>\n\n\n\n<li>\u03c0 = 3.14<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Volume of Remaining Solid<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cylinder volume:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><mo>=<\/mo><mn>3.14<\/mn><mo>\u00d7<\/mo><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>8<\/mn><mo>=<\/mo><mn>904.32<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\pi r^2h=3.14\\times6^2\\times8=904.32<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cone volume:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>3.14<\/mn><mo>\u00d7<\/mo><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>8<\/mn><mo>=<\/mo><mn>301.44<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac13\\pi r^2h=\\frac13\\times3.14\\times6^2\\times8=301.44<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Remaining volume:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>904.32<\/mn><mo>\u2212<\/mo><mn>301.44<\/mn><mo>=<\/mo><mn>602.88<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">904.32-301.44=602.88\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Total Surface Area<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Slant height:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><msqrt><mrow><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>8<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>10<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">l=\\sqrt{6^2+8^2}=10\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Surface Area:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Surface<\/th><th>Area (cm\u00b2)<\/th><\/tr><tr><td>Curved surface of cylinder<\/td><td>301.44<\/td><\/tr><tr><td>Bottom circular base<\/td><td>113.04<\/td><\/tr><tr><td>Curved surface of cone<\/td><td>188.40<\/td><\/tr><tr><td>Total<\/td><td>602.88<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Volume = 602.88 cm\u00b3<\/li>\n\n\n\n<li>Total Surface Area = 602.88 cm\u00b2<\/li>\n<\/ul>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-9\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-10\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-10\" hidden>Show More<\/button><\/section>\n\n\n<details class=\"accrd-accordion\"><summary class=\"accrd-summary\"><span class=\"accrd-summary-text\">Answer<\/span><span class=\"accrd-icon\" aria-hidden=\"true\"><\/span><\/summary><div class=\"accrd-body\">\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Internal diameter = 6 cm \u21d2 r = 3 cm<\/li>\n\n\n\n<li>External diameter = 10 cm \u21d2 R = 5 cm<\/li>\n\n\n\n<li>Cone radius = 7 cm<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of hollow hemispherical shell:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>R<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><msup><mi>r<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{2}{3}\\pi(R^3-r^3)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><msup><mn>5<\/mn><mn>3<\/mn><\/msup><mo>\u2212<\/mo><msup><mn>3<\/mn><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mn>196<\/mn><mi>\u03c0<\/mi><\/mrow><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{2}{3}\\pi(5^3-3^3)=\\frac{196\\pi}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of cone:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>7<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mi>h<\/mi><mo>=<\/mo><mfrac><mrow><mn>49<\/mn><mi>\u03c0<\/mi><mi>h<\/mi><\/mrow><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac13\\pi(7)^2h=\\frac{49\\pi h}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Equating volumes:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>49<\/mn><mi>\u03c0<\/mi><mi>h<\/mi><\/mrow><mn>3<\/mn><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>196<\/mn><mi>\u03c0<\/mi><\/mrow><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{49\\pi h}{3}=\\frac{196\\pi}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>4<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">h=4\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: 4 cm<\/p>\n\n\n\n<\/div><\/details>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"true\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-11\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-11\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-12\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A solid metallic sphere of diameter 21 cm is melted and recast into smaller cones, each having diameter 3.5 cm and height 3 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sphere radius = 10.5 cm<\/li>\n\n\n\n<li>Cone radius = 1.75 cm<\/li>\n\n\n\n<li>Cone height = 3 cm<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Volume of the sphere<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>10.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{4}{3}\\times\\frac{22}{7}\\times(10.5)^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mn>4851<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=4851\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Volume of one cone<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{1}{3}\\pi r^2h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>1.75<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{1}{3}\\times\\frac{22}{7}\\times(1.75)^2\\times3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>7<\/mn><mn>4<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><mo>=<\/mo><mfrac><mn>77<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mn>9.625<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{22}{7}\\times\\left(\\frac{7}{4}\\right)^2=\\frac{77}{8}=9.625\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Number of cones<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mfrac><mn>4851<\/mn><mn>9.625<\/mn><\/mfrac><mo>=<\/mo><mn>504<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4851}{9.625}=504<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">504 cones can be formed.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-12\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-13\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-13\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-14\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Formula<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Volume\u00a0of\u00a0sphere<\/mtext><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Volume of sphere}=\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the metal is melted, the total volume remains the same.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>1.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4}{3}\\pi(3)^3=\\frac{4}{3}\\pi(1.5)^3+\\frac{4}{3}\\pi(2)^3+\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cancel the common factor <math><semantics><mrow><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4}{3}\\pi<\/annotation><\/semantics><\/math> which is cancel out in both LHS and RHS. Then, <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><msup><mn>3<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><msup><mn>1.5<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">3^3=1.5^3+2^3+r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>27<\/mn><mo>=<\/mo><mn>3.375<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">27=3.375+8+r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><msup><mi>r<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mn>27<\/mn><mo>\u2212<\/mo><mn>11.375<\/mn><mo>=<\/mo><mn>15.625<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">r^3=27-11.375=15.625<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mroot><mn>15.625<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>2.5<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">r=\\sqrt[3]{15.625}=2.5\\text{ cm}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The radius of the third spherical ball is 2.5 cm.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-14\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"true\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-15\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A spherical ball of diameter 21 cm is melted and recast into cubes, each of side 1 cm. Find the number of cubes so formed.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-15\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-16\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A spherical ball of diameter 21 cm is melted and recast into cubes of side 1 cm.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Radius of the sphere<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mfrac><mn>21<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>10.5<\/mn><mtext>\u00a0cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">r=\\frac{21}{2}=10.5\\text{ cm}<\/annotation><\/semantics><\/math> <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Volume of the sphere<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>10.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{4}{3}\\times\\frac{22}{7}\\times(10.5)^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mn>4851<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=4851\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Volume of one cube<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>=<\/mo><mn>1<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=(1)^3=1\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Number of cubes<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mfrac><mn>4851<\/mn><mn>1<\/mn><\/mfrac><mo>=<\/mo><mn>4851<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4851}{1}=4851<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer: 4851 cubes<\/h3>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-16\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"true\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-17\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">How many lead balls, each of radius 1 cm, can be made from a sphere of radius 8 cm?<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-17\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-18\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A sphere of radius 8 cm is melted to make lead balls, each of radius 1 cm.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Formula<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Volume of a sphere:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since the metal is melted, the total volume remains the same.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Number\u00a0of\u00a0balls<\/mtext><mo>=<\/mo><mfrac><mrow><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>8<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><mrow><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Number of balls}=\\frac{\\frac{4}{3}\\pi(8)^3}{\\frac{4}{3}\\pi(1)^3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cancel the common terms:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><msup><mn>8<\/mn><mn>3<\/mn><\/msup><msup><mn>1<\/mn><mn>3<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>512<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{8^3}{1^3}=512<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">512 lead balls can be made.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-18\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"true\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-19\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-19\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-20\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm. The water level rises by 5.6 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Radius of marble = 0.7 cm<\/li>\n\n\n\n<li>Radius of beaker = 3.5 cm<\/li>\n\n\n\n<li>Rise in water level = 5.6 cm<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Volume of water displaced<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The rise in water level equals the volume of the marbles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V=\\pi r^2h<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>3.5<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>5.6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{22}{7}\\times(3.5)^2\\times5.6<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mn>215.6<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=215.6\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Volume of one marble<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V=\\frac{4}{3}\\pi r^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>0.7<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{4}{3}\\times\\frac{22}{7}\\times(0.7)^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>2156<\/mn><mn>1500<\/mn><\/mfrac><mo>\u2248<\/mo><mn>1.437<\/mn><msup><mtext>\u00a0cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">=\\frac{2156}{1500}\\approx1.437\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Number of marbles<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mfrac><mn>215.6<\/mn><mn>1.437<\/mn><\/mfrac><mo>=<\/mo><mn>150<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{215.6}{1.437}=150<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">150 marbles should be dropped into the beaker.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-20\" hidden>Show More<\/button><\/section>","protected":false},"excerpt":{"rendered":"<p>The volume and surface area are the important chapter of CBSE Board of Class 10. We are picking up most [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":73,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[3],"tags":[],"class_list":["post-49","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"The volume and surface area are the important chapter of CBSE Board of Class 10. 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