Problems on Volumes

1.

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

2.

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

3.

How many box's of length 40 Cm, width 30 Cm and height 10 Cm can be formed from a box of 6 m length, 4 m width and 2 m height.

   A.) 400
   B.) 3500
   C.) 4000
   D.) 2000

Answer: Option 'C'

(600×400×200)/(40×30×10) = 4000

4.

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

5.

The radius ofa cone is 14 m, slant height is 20 m. Find the curved surface area? 

   A.) 888 m2
   B.) 880 m3
   C.) 850 m3
   D.) 880 m2

Answer: Option 'D'

Cone curved surface area = πrl 
22/7 × 14 × 120 = 44 × 20 = 880 m2

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 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

8.

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%

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.

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

11.

How many cones of radius 4 m, height 2 m can be formed from a cylinder of 12 m radius, 10 m height: 

   A.) 125
   B.) 120
   C.) 135
   D.) 140

Answer: Option 'C'

(Cylinder volume)/(Cone volume) 
(πr2h)/(1/3 πr2h) = (π × 12 × 12 × 10)/(1/3 π × 4 × 4 × 2) = 135

12.

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

13.

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

14.

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

15.

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

16.

If each edge of cube increased by 10%, the percentage increase in surface area is: 

   A.) 33.1%
   B.) 33%
   C.) 32.2
   D.) 32.3

Answer: Option 'A'

100 × (110)/100 × (110)/100 × (110)/100 => 1331/100 = 33.1%

17.

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

18.

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

19.

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

20.

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

21.

The radius of a cone is 8 m, height 6 m. Find the slant height? 

   A.) 10 Cm
   B.) 15 Cm
   C.) 10 m
   D.) 15 m

Answer: Option 'B'

Answer: Option 'B'
Cone slant height (l) = √r2+h2 
= √64+36 = 10 m.

22.

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%

23.

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

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.

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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