### Volume & Surface

1) The surface area of a cube is 600 cm2. The length of its diagonal is

- cm
- cm
- 10 cm
- 10 cm

2) The length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high, is

- 30 m
- 15 m
- 30 m
- 60 m

3) The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.

- 150
- 140
- 120
- 100

- 48 cm
^{2} - 40 cm
^{2} - 36 cm
^{2} - 32 cm
^{2}

5) A water tank is 30 m long, 20 m wide and 12 m deep. It is made of iron sheet which is 3 m wide. The tank is open at the top. If the cost of iron sheet is Rs. 10 per meter, what is the total cost of iron sheet required to build the tank?

- Rs. 6000
- Rs. 8000
- Rs. 9000
- Rs. 10,000

6) In a shower 10 cm of rain falls. What is the volume of water that falls on 1.5 hectares of ground?

- 1500 m
^{3} - 1400 m
^{3} - 1200 m
^{3} - 1000 m
^{3}

7) The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, find the surface of the cube.

- 14,400 cm
^{2} - 44,200 cm
^{2} - 57,600 cm
^{2} - 86,400 cm
^{2}

8) Surface area of a sphere is 5544 cm2. Its volume will be

- 30808 cm
^{3} - 38808 cm
^{3} - 380808 cm
^{3} - 380800 cm
^{3}

9) If two spheres have their radii in the ratio 2: 3, the ratio of their volumes is

- 8 : 27
- 4 : 9
- 6 : 12
- 1 : 15

10) The radius of hemisphere is 3 cm. The ratio of its volume to the total surface area is

- 1: 3
- 2: 1
- 1: 1
- 2: 3

11) If the curved surface area of a sphere is same as the curved surface area of a hemisphere, find the radius of the hemisphere.

- Same as that of the sphere.
- times that of the sphere.
- times that of the sphere.
- 2 times that of the sphere.

12) The radii of two cylinders are in the ratio of 2: 3 and their heights are in the ratio of 5: 3. The ratio of their volume is

- 4: 9
- 9: 4
- 20: 27
- 20: 25

13) The radius of road roller is 1 meter and length 7/22 meter. When it is rolled on a ground then it rolls 500 times to level the ground. But it was found that on 5% part of the ground, roller rolled twice. What is the total area of the ground?

- 1000/Π
^{2}m^{2} - 975 m
^{2} - 975 m
^{2} - 950 m
^{2}

14) A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is

- 9 m
- 12 m
- 18 m
- 36 m

15) A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cylinder of base diameter 8 cm. What is the height of the cylinder?

- 4.5 cm
- 4.57 cm
- 4.67 cm
- 4.7 cm

16) The length, breadth, and height of a brick are 10 cm, 4 cm, and 3 cm, respectively. Find the surface area of the brick?

- 154 cm
^{2} - 156 cm
^{2} - 160 cm
^{2} - 164 cm
^{2}

17) A 6 m long and 4 m wide cistern contains water up to a breadth of 1 m 25 cm. Find the total surface area of the surface immersed in water?

- 42 m
^{2} - 49 m
^{2} - 52 m
^{2} - 64 m
^{2}

18) A boat of length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets into it. What is the mass of the man?

- 50 Kg
- 60 Kg
- 70 Kg
- 80 Kg

19) A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on deeper side. Find the volume of the swimming pool?

- 260
- 262
- 270
- 272

20) The cost of the paint is Rs. 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side

- 850
- 860
- 876
- 886

21) How many bricks, each measuring 25cm*11.25cm*6cm, will be needed to build a wall 8m*6m*22.5m?

- 610000
- 620000
- 630000
- 640000

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