Class 9 Surface Areas and Volumes Important Questions

Important Questions

Surface Areas and Volumes Important Questions

1. A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent. If the cost of 1 m² canvas is ₹ 70, find the cost of canvas required to make the tent.
2. A man uses a piece of canvas having an area of 551 m², to make a conical tent of base radius 7 m. Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately 1 m², find the volume of the tent that can be made with it.
3. The paint in a certain container is sufficient to paint an area equal to 9.375 sq.m. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
4. The surface area of a cube is 18(3/8). Find its volume.
5. The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost of painting the vessel all over at 35 paise per cm².
6. Two solid spheres made of the same metal have weights 5920 g and 740 g respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.
7. A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What s the radius of the ball ?
8. The surface areas of two spheres are in the ratio 1 : 4. Find the ratio of their volumes.
9. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?
10. A well with inside diameter of 10 m 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.
11. How many litres of water flows out of a pipe having an area of cross section of 5 cm² in 1 minute, if the speed of water in the pipe is 30 cm/sec ?
12. A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5cm through which water flows at the rate of 2 m per second. In how much time will the tank be filled?
13. Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see Fig. 13.5). Find how much he would spend for the tiles, if the cost of the tiles is Rs.360 per dozen.
14. The difference between inside and outside surfaces of a cylindrical tube 14 cm long, is 88 cm² . If the volume of the tube is 176 cm³ , find the inner and outer radii of the tube.
15. How many meter of cloth, 5 m wide, will be required to make a conical tent, the radius of whose base is 7 m and height is 24 m ?
16. The radius and the height of a right circular cone are in the ratio of 5 : 12 and its volume is 2512 cu cm. Find the curved surface area and the total surface area of the cone.(Use π = 3.14)
17. A semicircle sheet of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup. (Use √3 = 1.732)
18. A conical tent is to accommodate 11 persons. Each persons must have 4 m² of the space on the ground and 20 m³ of air to breath. Find the height of the tent.
19. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 of the volume of the given cone, at what height above the base, the section has been made?