## Volume and Surface Area of Solid Figures

#### Volume and Surface Area of Solid Figures

1. The volume of a cube is 512 cm3, Its surface area is ?
1. 64 cm2
2. 256 cm2
3. 384 cm2
4. 512 cm2

1. ∵ a3 = 512 = 8 x 8 x 8
⇒ a = 8 cm
∵ Surface area = 6a2

##### Correct Option: C

∵ a3 = 512 = 8 x 8 x 8
⇒ a = 8 cm
∵ Surface area = 6a2
=[6 x (8)2] cm2
=384 cm2

1. The surface area of a cube is 726 m2. Its volume is ?
1. 1300 m3
2. 1331 m3
3. 1452 m3
4. 1542 m3

1. Surface area = 6a2 = 726

##### Correct Option: B

Surface area = 6a2 = 726
⇒ a2 = 121
⇒ a = 11 cm
∴ Volume of the cube = (11 x 11 x 11) cm3
= 1331 cm3

1. If each side of a cube is doubled, then its volume? .
1. Is doubled
2. Becomes 4 times
3. Becomes 6 times
4. Becomes 8 times

1. Let the edge of original cube = x cm
Edge of new cube = (2x) cm
Ratio of their volumes = x3 : (2x)3

##### Correct Option: D

Let the edge of original cube = x cm
Edge of new cube = (2x) cm
Ratio of their volumes = x3 : (2x)3
= x3 : 8x3
= 1 :8

Thus the volumes be comes 8 times.

1. Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube. The length of the edge of this cube, is ?
1. 6 cm
2. 8 cm
3. 10 cm
4. None of these

1. Volume of new cube = (5)3 + (4)3 + (3)3 cm3

##### Correct Option: A

Volume of new cube = (5)3 + (4)3 + (3)3 cm3
= 126 cm3

Edge of this cube = (6 x 6 x 6)1/3 = 6 cm

1. If the volumes of two cubes are in the ratio 8 : 1, the ratio of their edges, is ?
1. 8 : 1
2. 2√2 : 1
3. 2 : 1
4. None of these

1. Volume of new cube = [(5)3 + (4)3 + (3)3] cm3

##### Correct Option: A

Volume of new cube = [(5)3 + (4)3 + (3)3] cm3
= 216 cm3
Edge of this cube = ( 6 x 6 x 6)1/3 = 6 cm