RRB NTPC - Problems on Volumes

1.

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

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

8.

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.

9.

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

10.

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

11.

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

12.

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

13.

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

14.

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

15.

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

16.

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

17.

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

18.

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

19.

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

20.

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


Volumes in Mensuration Download Pdf

Recent Posts