# Problems on Volumes

16.

The radius of hemi-sphere is 14 m. find its cutved surface area?

A.) 1332 sq.units
B.) 1213 sq.units
C.) 1233 sq.units
D.) 1232 sq.units

Curved surface area = 2πr2
2 (22/7) × 14 × 14
44 × 28
1238 sq.units

17.

A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is:

A.) 3 : 1
B.) 3 : 2
C.) 2 : 1
D.) None of these

Volume of the cylinder = πr2
Volume of the cone = 1/3 πr2
(πr2h)/(1/3 πr2h) = 3/1 = 3 : 1

18.

The radius of a cylinder is 6 m, height 21 m. The total surface area of the cylinder is?

A.) 528 Cm3
B.) 538 Cm3
C.) 527 Cm3
D.) 528 Cm2

Total surface area of the cylinder is = 2πr (r+h)
= 2 × 22/7 × 6(6+8)
= 2 × 22/7 × 6(14) = 44 × 12 = 528 m2

19.

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

20.

If the volume and surface area of a sphere are numerically the same, then its radius is:?

A.) 4
B.) 3
C.) 2
D.) 5

4/3 πr3 = 4 π r2
r = 3

21.

If the radius of the sphere is 14 m. then its total surface area is:

A.) 2464
B.) 2364
C.) 2465
D.) 2461

Sphere Total surface area = 4πr2 = 4 × 22/7 × 14 × 14 = 2464

22.

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

23.

The radius of the cylinder and cone are equal. find its volumes ratio:

A.) 1 : 3
B.) 3 : 1
C.) 2 : 1
D.) 3 : 2

radius of the cylinder = radius of the cone
πr2h = 1/3 πr2h 1 : 1/3
3 : 1

24.

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

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

• ## Important Mensuration Formulas

25.

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

26.

Two cylinders of theis radius in the ratio 3 : 5 and heights in the ratio 10 : 9. Then find the volumes ratio?

A.) 5 : 2
B.) 5 : 3
C.) 2 : 3
D.) 2 : 5

πR2H : πr2
9 × 10 : 25 × 9
90 : 225
2 : 5

• ## Important Mensuration Formulas

27.

Find the volume of cuboid 15 m length, 9 m breadth and 2 m height.

A.) 1420 m3
B.) 1440 m2
C.) 1424 m3
D.) 1440 m3

Cuboid volume => l × b × h => 15 × 12 × 8 = 1440 m3

28.

The radius of hemi sphere 7 m, find its volume?

A.) 205 1/4 m3 cubic units
B.) 205 1/3 m3 cubic units
C.) 205 1/3 m2 cubic units
D.) None of these

Hemi-sphere volume (V) = 2/3 πr3
= 2/3 × 22/7 × 7 × 7 × 7
= (44 × 49)/3 = 616/3 = 205 1/3 m3 cubic units

29.

How many cubes of 10 Cm edge can be put in a cubic box of 1 m edge?

A.) 100
B.) 10
C.) 1000
D.) 10000