{"id":800288,"date":"2023-12-09T10:50:29","date_gmt":"2023-12-09T05:20:29","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=800288"},"modified":"2023-12-09T10:50:29","modified_gmt":"2023-12-09T05:20:29","slug":"volume-and-surface-area-questions","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/volume-and-surface-area-questions\/","title":{"rendered":"20+ Volume and Surface Area Questions and Answers | Quantitative Aptitude"},"content":{"rendered":"\n<p>Understanding volume and surface area questions is crucial for understanding and solving various problems and concepts you might come across during your exams like <strong><a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/upsc-cse\/\">UPSC CSE<\/a><\/strong>, <strong><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/nda-exam-syllabus\/\">NDA<\/a><\/strong>, <a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/upsc-cds-exam-dates\/\"><strong>CDS<\/strong><\/a>, \u00a0<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/banking\/\"><strong>banking exams<\/strong><\/a>\u00a0( <a href=\"https:\/\/leverageedu.com\/blog\/bank-po\/\"><strong>SBI PO<\/strong><\/a>, <strong>RBI Assistant<\/strong>, <a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/ibps-rrb\/\"><strong>IBPS RRB<\/strong><\/a>) and Management Exams like the\u00a0<a href=\"https:\/\/leverageedu.com\/blog\/category\/cat\/\"><strong>CAT Exam<\/strong><\/a>. Whether you&#8217;re a school student preparing for competitive exams or simply someone curious about the world around you, mastering these fundamental ideas is essential.<\/p>\n\n\n\n<p>This article serves as your one-stop guide, with 20+ volume and surface area questions along with detailed solutions and explanations, including step-by-step instructions. By diving into these examples, you&#8217;ll gain the knowledge and confidence to conquer any challenge related to these key geometric concepts.<\/p>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-formula-of-surface-area-and-volume\">Formula of Surface Area and Volume<\/h2>\n\n\n\n<p>Before we go to Volume and Surface Area Questions the questions, let&#8217;s have a look at the important formulas:<\/p>\n\n\n\n<p>Volume:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cuboid: l \u00d7 b \u00d7 h<\/li>\n\n\n\n<li>Cube: a^3<\/li>\n\n\n\n<li>Cylinder: \u03c0r^2h<\/li>\n\n\n\n<li>Cone: (1\/3)\u03c0r^2h<\/li>\n\n\n\n<li>Sphere: (4\/3)\u03c0r^3<\/li>\n\n\n\n<li>Pyramid: (1\/3) \u00d7 base area \u00d7 height<\/li>\n<\/ul>\n\n\n\n<p>Surface Area:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cuboid: 2(lb + bh + hl)<\/li>\n\n\n\n<li>Cube: 6a^2<\/li>\n\n\n\n<li>Cylinder: 2\u03c0r^2 + 2\u03c0rh (lateral + base)<\/li>\n\n\n\n<li>Cone: \u03c0r^2 + \u03c0rl (lateral + base)<\/li>\n\n\n\n<li>Sphere: 4\u03c0r^2<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-practise-these-volume-and-surface-area-questions\">Practise these Volume and Surface Area Questions<\/h2>\n\n\n\n<p>Now, buckle up and prepare to master volume and surface area questions with these 20+ questions and answers:<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Cuboids and Cubes:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Find the volume of a cuboid with length 10 cm, breadth 5 cm, and height 8 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Volume of a cuboid = l \u00d7 b \u00d7 h<\/li>\n\n\n\n<li>Step 2: Substitute the given values: Volume = 10 cm \u00d7 5 cm \u00d7 8 cm<\/li>\n\n\n\n<li>Step 3: Calculate the result: Volume = 400 cm^3<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the volume of the cuboid is 400 cm^3.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Calculate the surface area of a cube with side length 7 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Surface area of a cube = 6a^2<\/li>\n\n\n\n<li>Step 2: Substitute the given value: Surface area = 6 \u00d7 7 cm^2<\/li>\n\n\n\n<li>Step 3: Calculate the result: Surface area = 294 cm^2<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the surface area of the cube is 294 cm^2.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>A cuboid has a volume of 240 cm^3 and a base area of 40 cm^2. Find its height.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Volume = l \u00d7 b \u00d7 h<\/li>\n\n\n\n<li>Step 2: Rearrange the formula to solve for height: h = Volume \/ Base area<\/li>\n\n\n\n<li>Step 3: Substitute the given values: h = 240 cm^3 \/ 40 cm^2<\/li>\n\n\n\n<li>Step 4: Calculate the result: h = 6 cm<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the height of the cuboid is 6 cm.<\/p>\n\n\n\n<p class=\"has-electric-grass-gradient-background has-background\"><strong>Also Read:\u00a0<\/strong><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/questions-of-syllogism-reasoning\/\"><strong>Questions of Syllogism Reasoning | Verbal Reasoning<\/strong><\/a><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Cylinders and Cones:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li>Determine the volume of a cylinder with radius 4 cm and height 12 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Volume of a cylinder = \u03c0r^2h<\/li>\n\n\n\n<li>Step 2: Substitute the given values: Volume = \u03c0 \u00d7 (4 cm)^2 \u00d7 12 cm<\/li>\n\n\n\n<li>Step 3: Calculate the result: Volume = 192\u03c0 cm^3<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the volume of the cylinder is 192\u03c0 cm^3.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li>Calculate the lateral surface area of a cone with radius 5 cm and slant height 13 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Lateral surface area of a cone = \u03c0rl<\/li>\n\n\n\n<li>Step 2: Substitute the given values: Lateral surface area = \u03c0 \u00d7 5 cm \u00d7 13 cm<\/li>\n\n\n\n<li>Step 3: Calculate the result: Lateral surface area = 65\u03c0 cm^2<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the lateral surface area of the cone is 65\u03c0 cm^2.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li>A cylindrical water tank has a diameter of 100 cm and a height of 150 cm. How much water can it hold?<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Convert diameter to radius: radius = diameter \/ 2 = 100 cm \/ 2 = 50 cm<\/li>\n\n\n\n<li>Step 2: Identify the<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Spheres:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"7\">\n<li>Find the volume of a sphere with radius 6 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Volume of a sphere = (4\/3)\u03c0r^3<\/li>\n\n\n\n<li>Step 2: Substitute the given value: Volume = (4\/3)\u03c0 \u00d7 (6 cm)^3<\/li>\n\n\n\n<li>Step 3: Calculate the result: Volume = 288\u03c0 cm^3<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the volume of the sphere is 288\u03c0 cm^3.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"8\">\n<li>Calculate the surface area of a sphere with radius 5 cm.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Surface area of a sphere = 4\u03c0r^2<\/li>\n\n\n\n<li>Step 2: Substitute the given value: Surface area = 4\u03c0 \u00d7 (5 cm)^2<\/li>\n\n\n\n<li>Step 3: Calculate the result: Surface area = 100\u03c0 cm^2<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the surface area of the sphere is 100\u03c0 cm^2.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"9\">\n<li>A spherical balloon has a surface area of 144\u03c0 cm^2. Find its radius.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Surface area of a sphere = 4\u03c0r^2<\/li>\n\n\n\n<li>Step 2: Rearrange the formula to solve for radius: r^2 = Surface area \/ 4\u03c0<\/li>\n\n\n\n<li>Step 3: Substitute the given value: r^2 = 144\u03c0 cm^2 \/ 4\u03c0<\/li>\n\n\n\n<li>Step 4: Calculate the radius: r = \u221a(36 cm^2) = 6 cm<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the radius of the spherical balloon is 6 cm.<\/p>\n\n\n\n\n\n<p class=\"has-medium-font-size\"><strong>Mixed Questions:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"10\">\n<li>A rectangular box has a length of 15 cm, breadth of 10 cm, and height of 8 cm. What is the total surface area?<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Total surface area of a cuboid = 2(lb + bh + hl)<\/li>\n\n\n\n<li>Step 2: Substitute the given values: Total surface area = 2(15 cm \u00d7 10 cm + 10 cm \u00d7 8 cm + 15 cm \u00d7 8 cm)<\/li>\n\n\n\n<li>Step 3: Calculate the result: Total surface area = 680 cm^2<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the total surface area of the rectangular box is 680 cm^2.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"11\">\n<li>A right circular cone has a diameter of 16 cm and a height of 12 cm. Find its volume and lateral surface area.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Convert diameter to radius: radius = diameter \/ 2 = 16 cm \/ 2 = 8 cm<\/li>\n\n\n\n<li>Step 2: Identify the relevant formulas:\n<ul class=\"wp-block-list\">\n<li>Volume of a cone = (1\/3)\u03c0r^2h<\/li>\n\n\n\n<li>Lateral surface area of a cone = \u03c0rl<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Step 3: Substitute the given values:\n<ul class=\"wp-block-list\">\n<li>Volume = (1\/3)\u03c0 \u00d7 (8 cm)^2 \u00d7 12 cm<\/li>\n\n\n\n<li>Lateral surface area = \u03c0 \u00d7 8 cm \u00d7 13 cm (where slant height is calculated using the Pythagorean theorem)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Step 4: Calculate the results:\n<ul class=\"wp-block-list\">\n<li>Volume = 64\u03c0 cm^3<\/li>\n\n\n\n<li>Lateral surface area = 104\u03c0 cm^2<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the volume of the cone is 64\u03c0 cm^3 and the lateral surface area is 104\u03c0 cm^2.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"12\">\n<li>A cylindrical vessel has a radius of 7 cm and a height of 14 cm. It is filled with water up to a height of 10 cm. Calculate the volume of water in the vessel.<\/li>\n<\/ol>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: Identify the relevant formula: Volume of a cylinder = \u03c0r^2h<\/li>\n\n\n\n<li>Step 2: Calculate the volume of the cylinder: Volume = \u03c0 \u00d7 (7 cm)^2 \u00d7 14 cm = 308\u03c0 cm^3<\/li>\n\n\n\n<li>Step 3: Calculate the volume of the empty space above the water: Volume = \u03c0 \u00d7 (7 cm)^2 \u00d7 4 cm = 196\u03c0 cm^3<\/li>\n\n\n\n<li>Step 4: Calculate the volume of water by subtracting the empty space from the total volume: Volume of water = 308\u03c0 cm^3 &#8211; 196\u03c0 cm^3 = 112\u03c0 cm^3<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the volume of water in the vessel is 112\u03c0 cm^3.<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color\"><strong>RELATED POSTS<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/questions-of-letter-and-symbol-series\/\"><strong>45+ Questions of Letter and Symbol Series with Answers<\/strong><\/a><\/td><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-blood-relation-reasoning-questions\/\"><strong>Blood Relation Reasoning Questions | Verbal Reasoning<\/strong><\/a><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-questions-of-series-completion-reasoning\/\"><strong>Series Completion Reasoning | Verbal Reasoning<\/strong><\/a><\/td><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/blog\/reasoning-questions\/\"><strong>Types of Reasoning Questions in Competitive Exams<\/strong><\/a><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-questions-of-direction-sense-test-reasoning\/\"><strong>Questions of Direction Sense Test Reasoning | Verbal Reasoning<\/strong><\/a><\/td><td class=\"has-text-align-center\" data-align=\"center\"><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-questions-of-arithmetic-reasoning\/\"><strong>20+ Questions of Arithmetic Reasoning | Verbal Reasoning<\/strong><\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>This was all about the \u201c20 + Area and Perimeter Questions and Answers\u201d. For more such informative blogs, check out our <a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/study-material\/\">Study Material Section<\/a>, or you can learn more about us by visiting our <a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/\">Indian exams<\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"Understanding volume and surface area questions is crucial for understanding and solving various problems and concepts you might&hellip;\n","protected":false},"author":68,"featured_media":800296,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[369,484,396],"tags":[],"class_list":{"0":"post-800288","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-indian-exams","8":"category-quantitative-aptitude","9":"category-study-material"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - 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