RRB NTPC - Problems on Volumes

  • 1. 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

  • 2. 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

  • 3. 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

  • 4. 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

  • 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 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 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. 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

  • 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. 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

  • 11. 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

  • 12. 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

  • 13. 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

  • 14. 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

  • 15. 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

  • 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. 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%

  • 18. 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

  • 19. 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

  • 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

  • 21. 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

  • 22. 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

  • 23. 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

  • 24. 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

  • 25. 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