APPSC Group 3 Mock Tests

Problems on Volumes  : Aptitude Test

  • 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



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