13. SURFACE AREAS AND VOLUMES
1. Find the ratio of surface area and volume of the sphere of unit radius. [Ans- 3:1]
2. If the radius of a sphere is doubled what will happen to its surface area?
[Ans- increases 4 times]
3. Find the length of longest rod that can be placed in a room 12m×9m×8m. [Ans-17m]
4. The lateral surface area of a cube is 576 cm2. Find its volume and TSA.
[Ans-1728 cm3, TSA-864cm2 ]
5. The length, breadth and volume of a cuboid are 80cm, 60cm and 19200 cu cm respectively. Find the height, lateral surface area and total surface area.
[Ans- h = 4cm, TSA = 10720cm2 ,CSA/LSA = 1120cm2]
6. A solid cube of edge 12 cm is cut into eight cubes of equal volume. What will be the edge of the new cube? Also find the ratio between the TSA of the new cube to that of the original cube. [Ans- edge = 6cm, ratio = 1:4]
7. The radius and slant height of a cone are in the ratio of 4:7. If its CSA is 792cm2, find its radius. [Ans- 12cm]
8. A right circular cylinder is just encloses a sphere of radius r. Find
(a). surface area of the sphere (b). CSA of cylinder. [Ans- a-4πr2, b-4πr2]
9. A cuboidal water tank is 5 m long, 3 m wide and 1.5 m deep. How many liters of water can it hold? [Ans- 27000 liters]
10. A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per cm3, find the mass of the shot-putt? [Ans- 3.85 kg]
11. A rectangular sheet of metal with dimension 66cm by 12cm is rolled to form a cylinder of height 12 cm. Find the volume of the cylinder. [Ans- 4158cm3]
12. A right triangle ABC with sides 5cm, 12cm and 13cm is revolved about the side 12cm. Find the volume of the solid so obtained. [Ans- 100π cm3]
13. A solid cylinder has TSA 462cm2. Its CSA is one third of its TSA. Find the volume of the cylinder. [Ans-239 cm3]
14. A semi-circular sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup. [Ans-622.31cm3]
15. The diameter of a garden roller is 1.4m and it is 2m long. How much area will it cover in 5 revolutions? [Ans- 44 m2]
16. A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(i) Which box has the greater CSA and how much? [Ans- Cube by 40m2]
(ii) Which box has the greater CSA and how much? [Ans- Cuboid by 10m2]
17. A joker’s cap is in the form of right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. [Ans- 550 cm2]
18. The floor of a rectangular hall has a perimeter 150m. If the cost of painting the four walls at the rate of Rs. 10 per m2 is Rs 9000, find the height of the wall. [Ans- 6m]
19. A river 3m deep and 40m wide is flowing at the rate of 2km/hr. How much water will fall into the sea in one minute?[Ans-4000m3]
20. A classroom is 10m long, 6.4m wide and 5m high. If each student be given 1.6m2 of the floor area, how many students can be accommodated in the room? How many cubic meter of air would each student get? [Ans-40 students, 8m3]
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= √( l²+b²+h²)
=√(12² + 9² + 8² )
=√( 144+81+64)
=√(289)
=17
Hence, longest rod that can be placed in a room of dimensions 12m x 9m x 8m is 17 m
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