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About This Booklet on Surface Areas and Volumes About This Booklet on Surface1 Areas and Volumes About This Booklet on Surface Areas and Volumes This Particular Booklet has been designed for the students of Math Class 10 (CBSE Board). However, it will also help those who have these chapters in their curriculum or want to gain the knowledge and explore the concepts. This Booklet explains: 1. Cube, Cuboid and Cylinder 2. Cone and Frustum 3. Sphere and Hemisphere 4. Combination of solids This Booklet also covers: 1. MCQs 2. Questions with Solutions 3. Questions for practice and 4. QR Codes to scan and watch videos on Surface Areas and Volumes QR codes when scanned with mobile scanner take you to our YouTube channel Let’sTute (www.youtube.com/letstute) where you can watch our free videos (need internet connection) on the topic. For Surface Areas and Volumes, in total, we have 8 videos which are accessible on several other platforms as described on the back cover of this Booklet. However, if there is any query, feel free to connect with us on the details given on the last page. Some other documents are also available: About Let’s Tute Let’sTute (Universal Learning Aid) is an E-learning company based in Mumbai, India. (www.letstute.com) We create content for Mathematics, Biology, Physics, Environmental Science, Book-Keeping & Accountancy and also a series on value education known as V2lead 2 13 .1 Cube, Cuboid and Cylinder Scan to watch the video on INTRODUCTION Surface area and Volume Surface Area: It is the sum of total exposed area of a three dimensional solid object. Its unit can be in the form cm2, m2 etc. Volume: It is the amount of space occupied by an object. Its unit can be cm3, m3, etc. Cuboid: A cuboid is the solid shape which has six rectangle faces at right angles to each other. Cube: A cube is a special form of cuboid which is bounded by six equal square faces. Right Circular Cylinder: A solid obtained by revolving a rectangular lamina about one of its sides, is called as Right Circular Cylinder. Total Surface Area and Volume for Cube, Cuboid and Cylinder MCQs (Multiple Choice Questions) 1. A cube is special type of cuboid. Scan to watch the video on A)True B)False Volume of cube, cuboid & cylinder 2. Volume of any object is nothing but its maximum capacity of storage. A)True B)False 3. A cube is three dimensional objects bounded by _ _ _ _ equal square faces. A)Five B)Six C)Four D) None of these 3 4. A cube of sides 6 m will have volume_ _ _ _ A)216 m2 B) 216 m3 C) 216 cm2 D) 216 m 5. If the radius of cylinder is doubled then the curved surface area of cylinder will be _ _ _ _ as compared to previous. A)Same B) Doubled C) Thrice D) None of these 6. What is the surface area of a cube having edges of length 15 cm? A)1350 B)225 C)1350 D) 1500 7. What iscm the length ofcm side of a cube ifcm the total surfacecm area of cube is 726 cm2? A)11 B)16 C)72 D) None of these 8. If thecm area of one face of cube cm is 169 cm2 thencm what will be the volume of cube. A) 1300 B) 4238 C) 5642 D) 2197 9. If the perimeter cm of onecm face of the cube is 28 cmcm then what willcm be its volume. A) 343 B) 343 C) 437 D) 473 10. What iscm the surface areacm of cuboid with cm dimension in m are cm 12×10×15 A) 1200 B) 900 C) 920 D) 940 11. Total Surfacem Area ofm Right Circularm Cylinder is _ _ _ _ m A) B) C) D) None of these 12. What 휋 ℎis the + curved surface 휋 areaℎ × of Cylinder 휋 ℎwhen − radius is 14 cm and height is 15 cm. [ π = 22/7] A) 1300 B) 2100 C) 1320 D) 4242 13. How many liters of water will be stored in a cylindrical tank of radius 3 m and height 7 m. [ Hint 1 m3 =1000 Liters take π = 22/7] A) 28640 B) 254000 C) 198000 D) None of these Answers: 퐿 퐿 퐿 1.(A), 2.(A), 3.(B), 4.(B), 5.(B), 6.(C), 7.(A), 8.(D), 9.(A) 10.(B) 11.(A) 12.(C) 13.(C) Solved Questions Q.1 Find the Total cost of painting the four walls of cuboidal room at the rate of 13 Rs per m2.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m. Given: For Cuboidal Room, Rate of Painting = 13 Rs/m2, l = 10m, b = 5m, h = 6m Solution: An Approach: As we have to paint only the walls, surface area of roof and floor so are not taken into calculation 4 Vertical surface area of cuboid (four walls) = = 2(10+5) × 6 + × 풉 h = 2(15) × 6 = 180 b Vertical surface area of cuboid = 180 m2. l Total cost of painting four walls = Vertical surface area of cuboid × Rate of painting wall/m2 = 180 m2 × 13 = 2340 Ans. Therefore Cost of Painting the four walls is Rs 2340 Q.2 A cuboidal pillar of dimension 600 cm × 55 cm × 25 cm made of wood which weights 200kg/m3. What will be the weight of the pillar? Given: Tips: Please remember to convert For Pillar [cuboid] dimensions from centimeter to meter as Length = 600cm = = 6m weight is given kg/m3. Breadth = 55cm = = 0.55m Height = 25cm = = 0.25m Solution: Volume of pillar [cuboid] = = 6 m × 0.55 m× 0.25 m = 0.825 × ×m 풉3 Weight of pillar = Volume of pillar × weight of volume per m3 = 0.825×200 = 165 Kg Ans. Weight of pillar =165 Kg Q.3 If the Diameter of a roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a playground. Find the area of playground in m2. Given: The Diameter of cylindrical roller = 40 cm =0.4m An Approach: Please try to analyze Radius of cylindrical roller(r) = = 20 cm= 0.2 m that 1 revolution = lateral surface area Length of cylindrical roller (h) =140 cm = 1.4 m of cylinder. So 350 revolution = Solution: × 휋ℎ Curved surface area of cylindrical roller = = 흅풓풉 = × × . × . = 1.76 m2 Area covered in one revolution × ×is .= curved × . surface area of cylinder = 1.76 m2 5 Total Area of Playground = No. of revolutions × curved surface area of cylinder = 350 × 1.76 m2 = 616 m2 Ans. Area of Playground = 616 m2 Q.4 The curved surface area of cylinder is 154 cm2. The total surface area of the cylinder is thrice the curved surface area. Find the volume of cylinder. Given: Curved surface area of cylinder ( ) = 154 cm2 [훑 = ] Solution: Total surface area of cylinder = 3휋 ×ℎ curved surface area 154 + 2πr2 = 462 휋 ℎ + 2 휋πr2 = 462= – × 154 2πr2 = 308 2 × r×= = 2 × r = 49 × r = 7 Curved surface area of cylinder ( ) = 154 cm2 흅풓풉 × × × ℎ =h = h = 3.5 cm × Volume of Cylinder = = 흅풓 풉 = 539 cm3 × × × . Ans. Volume of Cylinder = 539 cm3 Practice Yourself Q1. Find the length of edges of cube having volume 512 cm3. Ans: 8 cm Q2. A Gift box of length 15 cm, breadth 13cm and height 14 cm need to be covered with a decorative wrapper. Find the area of wrapper needed. Ans: 1174 cm2 Q3. If a gas cylinder has an inner radius of 14 cm and height of 70 cm. How much maximum amount of gas can be stored in that cylinder? [π = 22/7] Ans: 43120 cm3 6 Q4.What will be the radius of cylinder if the curved surface area of cylinder is 1760 cm2 and its height is 14 cm? Ans: 20 cm Q5. If curved surface area of cylinder is 1188 cm2 and radius is 21 cm. What will be its volume? [Hint: first find the height using curved surface area] Ans: 12474 cm3 Q6. Find the curved surface area of cylinder when radius is 14 cm and height is 2 cm more than double of its radius. Ans: 2640 cm2 Make your own notes: 7 13 .2 Cone and Frustum INTRODUCTION Cone: A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called vertex. We can also define it as, “A solid obtained by revolving a right angled triangular lamina about any side (except hypotenuse) is a right circular cone.” Slant Height of a Cone (l) = Curved surface area of Cone = Total Surface Area of Cone = 풉 + 풓 흅풓풍 Volume of Cone = 흅풓풓 + 풍 흅풓 풉 l = slant height, r = radius of cone Frustum: If the cone is cut off by a plane parallel to the base not passing through vertex then we get the lower base portion as a frustum of cone. Where r1 and r2 are the radii of the ends of frustum (r1>r2) h = height and l = slant height Slant Height of the Frustum (l) = Curved surface area of Frustum = 풉 + 풓 − 풓 Total Surface Area of Frustum = 흅풓 + 풓풍 Volume of Frustum = 흅풓 + 풓풍 + 흅풓 + 흅풓 흅풓 + 풓 + 풓 × 풓풉 MCQs (Multiple Choice Questions) 1. If the radii of both the ends of frustum are same then it is a cylinder. A) True B) False 2. The volume of a cone is one third of the volume of the cylinder. A) True B) False 3. What is surface area of a cone with radius 7 cm and slant height 12 cm? A) 184 cm2 B) 418 cm2 C) 184 cm2 D) 284 cm2 4.
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