RRB NTPC - Problems on Volumes

1.

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

2.

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

3.

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

4.

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

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 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

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.

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

9.

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

10.

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%

11.

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

12.

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%

13.

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

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 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

16.

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

17.

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

18.

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.

19.

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

20.

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


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