#### Chapter 18 Surface Area and Volume of a Cuboid and Cube R.D. Sharma Solutions for Class 9th MCQ's

**Multiple Choice Questions**

1. If A

_{ 1 },A

_{2 },and A

_{ 3 }denote the areas of three adjacent faces of a cubiod, then its volume is

(a) A

_{1 }A_{2 }A_{3}
(b) 2A

_{1 }A_{2 }A_{3}
(c ) √(A

_{1 }A_{2 }A_{3 })
(d) ∛(A

_{1 }A_{2 }A_{3 })**Solution**

2. The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is

(a) 10 cm

(b) 10√2 cm(c) 10√3 cm

(d) 20 cm

**Solution**

3. If l is the length of a diagonal of a cube of volume V, then

(a) 3V = l^{3}

(b) √3V = l

^{3}

(c) 3√3V = 2l

^{3}

(d) 3√3V = l

^{3}

**Solution**

4. Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is

(a) 7 : 9

(b) 49 : 81

(c) 9 : 7

(d) 27 : 23

**Solution**

5. If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then A/V

(a) x

(b) 1/2 (1/xy + 1/yz + 1/zx)^{2}y^{2}z^{2}(c) (1/x + 1/y + 1/z)

(d) 1/xyz

**Solution**

6. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is

(a) 361 cm^{2}

(b) 125 cm

^{2}

(c) 236 cm

^{2}

(d) 486 cm

^{2}

**Solution**

7. If the length of a diagonal of a cube is 8√3 cm, then its surface area is

(a) 512 cm^{2}

(b) 384 cm

^{2}

(c) 192 cm

^{2}

(d) 768 cm

^{2}

**Solution**

8. If each edge of a cube is increased by 50%, the percentage increase in its surface area is

(a) 50 %

(b) 75 %

(c) 100 %

(d) 125 %

**Solution**

9. If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is

(a) 8 : 1(b) 2√2:1

(c) 2 : 1

(d) none of these

**Solution**

10.The volume of a cube whose surface area is 96 cm

(a) 16√2cm^{2}, is^{3}

(b) 32 cm

^{3}

(c) 64 cm

^{3}

(d) 216 cm

^{3}

**Solution**

11. The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm3, the total surface area of the box is

(a) 27 cm^{2}

(b) 32 cm

^{2}

(c) 44 cm

^{2}

^{ }(d) 88 cm

^{2}

**Solution**

12. A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm

(a) 3.5 cm^{3}. The two cubes are then placed on top of a third cube whose volume is 8 cm^{3}. The height of the stacked cubes is(b) 3 cm

(c) 7 cm

(d) none of these

**Solution**

13. If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm

(a) 30 cm^{3}, then the length of the shortest edge is(b) 20 cm

(c) 15 cm

(d) 10 cm

**Solution**

14. If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

(a) 2 V

(b) 4 V

(c) 6 V

(d) 8 V

**Solution**

15. If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is

(a) 2 S

(b) 4 S

(c) 6 S

(d) 8 S

**Solution**

16. The area of the floor of a room is 15 m

(a) 60 dm^{2}. If its height is 4 m, then the volume of the air contained in the room is^{3}

(b) 600 dm

^{3}

(c) 6000 dm

^{3}

(d) 60000 dm

^{3}

**Solution**

17. The area of the floor of a room is 15 m

(a) 60 dm^{2}. If its height is 4 m, then the volume of the air contained in the room is^{3}

(b) 600 dm

^{3}

(c) 6000 dm

^{3}

(d) 60000 dm

^{3}

**Solution**

18. 10 cubic metres clay is uniformly spread on a land of area 10 ares. the rise in the level of the ground is

(a) 1 cm

(b) 10 cm

(c) 100 cm

(d) 1000 cm

**Solution**

19. Volume of a cuboid is 12 cm

(a) 24^{3}. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is(b) 48

(c) 72

(d) 96

**Solution**

20. If the sum of all the edges of a cube is 36 cm, then the volume (in cm

(a) 9^{3}) of that cube is(b) 27

(c) 219

(d) 729

**Solution**

21. The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm×9 cm×6 cm, is

(a) 9

(b) 10

(c) 18

(d) 20

**Solution**

22. On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

(a) 300 litres

(b) 450 litres

(c) 3000 litres

(d) 4500 litres

**Solution**