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

Answer: Option 'D'

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

Answer: Option 'A'

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

Answer: Option 'D'

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

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

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

Answer: Option 'B'

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

Answer: Option 'A'

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

Answer: Option 'A'

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

Answer: Option 'B'

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

Answer: Option 'B'

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

25.

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

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

Answer: Option 'D'

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

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

Answer: Option 'D'

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

Answer: Option ''

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

Answer: Option 'D'

(110×100×100)/10×10×10 = 1000

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