Problems on Volumes

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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