Assignment Volume and Surface Area of Solids

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1 Assignment Volume and Surface Area of Solids 1. (a) The diagonal of a cube is 16 3 cm. Find its surface area and volume. (b) The capacity of a cylindrical tank is 1848 m 3 and the diameter of its base is 14 m. Find the depth of the tank. (c) Total surface area of a cube is 726 cm 2. Find its volume. 2. (a) Find the length of the largest rod that can be placed in a room measuring 12 m 9 m 8 m. (b) The sum of the length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid. (c) The total surface area of a cylinder of radius 5 cm is 660 cm 2. Find the height of the cylinder. 3. (a) A room is half as long again as it is broad. The cost of carpeting the room at Rs 18 per m 2 is Rs 972 and the cost of white washing the four walls at Rs 6 per m 2 is Rs Find the dimensions of the room. (b) The radii of two right circular cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 4. Calculate the ratio of their curved surface areas. (c) How many planks each of which is 2 m long, 2.5 cm broad and 4 cm thick can be cut off from a wooden block 6 m long, 15 cm broad and 40 cm thick? 1

2 4. (a) A solid cube of side 12 cm is cut into 8 cube of equal volume. What will be the side of the new cube? (b) A cuboid has total surface area of 40 m 2 and its lateral surface area is 26 m 2. Find the area of its base. (c) A rectangular sheet of paper 44 cm 20 cm, is rolled along its length to form a cylinder. Find the volume of the cylinder so formed. 5. (a) Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid. (b) A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes. (c) The area of the base of a right circular cylinder is 154 cm 2 and its height is 15 cm. Find the volume of the cylinder. 6. (a) The area of a path is 6500 m 2. Find the cost of covering it with gravel 14 cm deep at the rate of Rs 5.60 per cubic metre. (b) The diameter of a 22.5 m deep well is 7 m. Find the cost of plastering the inner curved surface at Rs 4 per square metre. (c) Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube. 7. (a) The length of a cold storage is double its breadth. Its height is 3 m. The area of its four walls (including doors) is 108 m 2. Find its volume. (b) Find the number of bricks each measuring 25 cm 12.5 cm 7.5 cm required to construct a 6 m long, 5 m high and 0.5 m thick wall, while the cement and sand mixture occupies 1 20 of the volume of the wall. 2

3 8. (a) A metallic sheet is of the rectangular shape with dimensions 48 cm 36 cm. From each one of its corners a square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume of the box. (b) The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the ratio between the height and radius of the cylinder. 9. (a) The cross-section of a piece of metal 2 m in length is shown in the adjoining figure. Calculate (i) The area of its cross-section (ii) The volume of piece of metal (iii) The weight of piece of metal to the nearest kg, if 1 cm 3 of the metal weight 6.5 kg. (b) A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment. 10. (a) The water in a rectangular reservoir having a base 80 m 60 m, is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side 20 cm, if water runs through the pipe at the rate of 15 km/hr? (b) If the radius of the base of a right circular cylinder is halved keeping the height same. What is the ratio of the volume of the reduce cylinder to that of the original? 3

4 11. (a) The outer dimensions of a closed wooden box are 10 cm by 8 cm by 7 cm. Thickness of the wood is 1 cm. Find the total cost of wood required to make box, if 1cm 3 of wood cost Rs 2. (b) The volume of metallic cylindrical pipe is 748 cm 3. Its length is 14 cm and its external radius is 9 cm. Find its thickness. 4

5 Answers 1. (a) 1536 cm 2, 4096 cm 3 (b) 12 m (c) 1331 cm 3 2. (a) 17 m (b) 240 cm 2 (c) 16 cm 3. (a) l = 9 m, b = 6 m, h = 6 m (b) 5 : 6 (c) (a) 6 cm (b) 7 m 2 (c) 3080 cm 3 5. (a) 350 cm 2 (b) 384 cm 2 (c) 2310 cm 3 6. (a) Rs 5096 (b) Rs 1980 (c) 125% 7. (a) 216 m 3 (b) (a) 5120 cm 3 (c) 1 : 1 9. (a) (i) 162 cm 2 (ii) cm 3 (iii) 211 kg (b) 1.6 m 10. (a) 52 hrs (b) 1 : (a) Rs 640 (b) 1 cm 5

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