RRB NTPC - Problems on Volumes

1.

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

2.

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

3.

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

4.

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

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.

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

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 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

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.

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

11.

How many cuboids of length 5 m, width 3 m and height 2 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. 

   A.) 118
   B.) 106
   C.) 119
   D.) 108

Answer: Option 'D'

(18 × 15 × 12)/(5 × 3 × 2) = 108

12.

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

13.

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

14.

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

15.

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

16.

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

17.

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

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 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

20.

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%


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