# Problems on Volumes

• ## Important Mensuration Formulas

1.

The side of a cube is 8 m, Find the voiume?

A.) 513 m3
B.) 514 m3
C.) 512 m3
D.) 502 m3

Cube Volume = a3
a3 = 83 = 512 m3

2.

The side of a cube is 15 m, find it's surface area?

A.) 1350 m2
B.) 1250 m2
C.) 1300 m2
D.) 1450 m2

Surface area = 6 a2 sq. units
6 a2 = 6 × 225 = 1350 m2

3.

The side of a cube is 12 m, find the lateral surface area?

A.) 526 m2
B.) 506 m2
C.) 518 m2
D.) 516 m2

Lateral surface = 4 a2
4 × 122 = 4 × 144 => 516 m2

4.

The lateral surface area of cube is 100 sq.units. find the volume of cube?

A.) 122 m3
B.) 135 m3
C.) 125 m3
D.) 120 m3

Lateral surface = 4 a2 = 100 sq.units
a2 = 25
a = 5.
Cube volume = a3 => 125 m3

5.

The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube?

A.) 6 m
B.) 7 m
C.) 8 m
D.) 9 m

Cube volume = a3 cubic units
Surface area = 6 a2 sq.units
a3 = 6 a2
a = 6 m

6.

The surface area of a cube is 486 Cm3. Find its volume?

A.) 739 Cm3
B.) 529 Cm3
C.) 729 Cm3
D.) None of these

Let each edge of the cube be a Cm.
Then 6 a2 = 486 => a2 = 81 = 92 => a = 9
Volume = a3 = 93 Cm3 => 729 Cm3

7.

The diagonal of a cube is 8√3. find its volume and surface area.

A.) 34 Cm2
B.) 364 Cm3
C.) 384 Cm2
D.) 384 Cm3

√3.a = 8 √3 => a = 8
Volume = a3 => (8 × 8 × 8) Cm3 => 512 Cm3
Surface area => 6 a2 => (6 × 8 × 8) Cm2 => 384 Cm2

8.

Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube?

A.) 216 Cm2
B.) 256 Cm3
C.) 216 Cm3
D.) None of these

Volume of the new cube = [ 53 + 43 + 33 ] Cm3
= 125 + 64 + 27 = 216 Cm3 => a3 = 216 Cm3

9.

Two cubes of thire sides ratio 2 : 3. Find its cube volumes ratio?

A.) 27 : 7
B.) 27 : 8
C.) 8 : 27
D.) 8 : 25

a3 : b3 = 23 : 33
= 8 : 27

10.

Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:

A.) 5 : 4
B.) 4 : 5
C.) 3 : 5
D.) None of these