Problems on Volumes

1.

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

2.

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

3.

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

4.

If each edge of cube increased by 20%, the percentage increase in 

   A.) 44%
   B.) 34%
   C.) 48%
   D.) 42%

Answer: Option 'A'

100 × (120)/100 × (120)/100 = 144 => 44%

5.

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

6.

Two spheres of their radious in the ratio 4 : 3. Find its volumes ratio?

   A.) 64 : 26
   B.) 64 : 25
   C.) 64 : 27
   D.) None of these

Answer: Option 'C'

Sphere volume (V) = 4/3 πR3 : 4/3 π r3 = 43 : 33 = 64 : 27

7.

The radius of a cone is 4 m, height 5 m. Find the curved surface area?

   A.) 4 units
   B.) 5 units
   C.) 6 units
   D.) 3 units

Answer: Option 'B'

Cone curved surface area = πrl = 22/7 × 4 × 5 = 440/7 = 62 6/7 
Slant height (l) = √r2+h2 = √16+9 = √25 = 5

8.

The height of cylinder is 14 Cm and its diameter is 10 Cm. The volume of the cylinder is:

   A.) 110 Cm3
   B.) 1100 Cm3
   C.) 1101 Cm2
   D.) 1101 Cm3

Answer: Option 'B'

h = 14 Cm and r = 5 Cm 
Cylinder volume = πr2h = (22/7 × 5 × 5 × 14) Cm3 = 1100 Cm3

9.

The radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is: 

   A.) 1584 m3
   B.) 1582 m2
   C.) 1584 m2
   D.) None of these

Answer: Option 'C'

Lateral surface area = 2πrh 
= 2 × 22/7 × 12 × 21 
= 44 × 36 
= 1584 m2

10.

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

11.

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

12.

The length of box 12 Cm long, 8 Cm breadth and 9Cm height. Find the length of pencil in that box?

   A.) 17 Cm2
   B.) 18 Cm
   C.) 17 Cm
   D.) 18 Cm3

Answer: Option 'C'

Diagonal (d) = √l2+b2+h2 
= √122+82+92 
= √144+64+81 
= √289 => 17 Cm

13.

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

14.

The lateeral surface area of cuboid length 12 m, breadth 8 m and height 6m

   A.) 230 m3
   B.) 240 m3
   C.) 230 m2
   D.) 240 m2

Answer: Option 'D'

Cuboid lateral surface = 2h(l+b) 
= 2 × 6 (20) = 240 m2

15.

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

16.

The total surface area of a cuboid length 12 m, breadth 10 m and height 8 m. 

   A.) 592 m3
   B.) 592 m2
   C.) 594 m3
   D.) None of these

Answer: Option 'B'

Total surface area of cuboid 
= 2 (lb+bh+lh) 
= 2 (120 + 80+ 96) 
= 2 (296) => 596 m2

17.

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

18.

The radius of a cone is 10 m, height 21 m. The volume of the cone is:

   A.) 2220 m3
   B.) 2200 m2
   C.) 2200 m3
   D.) None of these

Answer: Option 'C'

1/3 πrh = 1/3 × 22/7 × 100 × 21 
= 2200 m3

19.

The height of a cylinder is 60 Cm and the diameter of its base is 5 Cm. The total surface area of the cylinder is : 

   A.) 981 Cm2
   B.) 982.13 Cm2
   C.) 982.14 Cm2
   D.) None of these

Answer: Option 'C'

Given h = 60 Cm and r = 5/2 Cm 
Total surface area = 2πrh + 2&pir2 
= 2πr(h+r) 
= [2 × 22/7 × 5/2 × (60 + 5/2)] Cm2 
= [ 44/7 × 5/2 × ( (120 + 5)/2 ) ] Cm2 
= 22/7 × 5 × 125/2 Cm2 
= (55 × 125)/7 Cm2 
= 6875/7 Cm2 
= 982.14 Cm2

20.

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

21.

The radius of hemi-sphere is 7 m. Find it's total surface area?

   A.) 452 m3
   B.) 462 m2
   C.) 462 m3
   D.) None of these

Answer: Option 'C'

otace area = 3πr2 sq.units 
= 3 × 22/7 × 7 × 7 
= 66 × 7 = 462 m3

22.

If the radius of sphere is doubled, then its volume is increased by: 

   A.) 100%
   B.) 200%
   C.) 700%
   D.) 800%

Answer: Option 'C'

radius = r. Original volume = 4/3 πr3
New radius = 2r New volume = 4/3 π(2r)3 = (32πr3)/3 
increase in volume = ( (32πr3)/3 × 3/(4πr3) × 100 ) % = 700%

23.

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

24.

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

25.

The radius of a cylinder is 10 m, height 14 m. The volume of the cylinder is: 

   A.) 4000 m2
   B.) 4300 m2
   C.) 4000 m3
   D.) None of these

Answer: Option 'C'

Cylinder volume = πr2h
= 22/7 × 10 × 10 × 14 
= 4400 m3


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