# 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

Answer: Option 'C'

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

Answer: Option 'A'

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

Answer: Option 'D'

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

Answer: Option 'C'

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

Answer: Option 'A'

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

Answer: Option 'C'

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

Answer: Option 'D'

√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

Answer: Option 'C'

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

Answer: Option 'C'

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

Answer: Option 'B'

The ratio of their surface area is
64 : 125
4 : 5

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