Volume of a Cube | Mensuration | Assessment | English | Grade 8

The volume of a cube whose edge is 25 cm is ______.

• 15675 cm³

• 15625 cm³

• 15680 cm³

• 15690 cm³

Answer explanation

Option 2 is correct. Volume of a cube = l³ = 25 × 25 × 25 = 15625 cm³

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If the volume of a cube is 216 m³, then its edge is ______.

• 9 m

• 7 m

• 11 m

• 6 m

Answer explanation

Option 4 is correct. Volume of a cube = l³ 216 m³ = l³ so, l = ∛216 = 6 m

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The volume of a cube is 729 cm³. Its total surface area is _______.

• 81 cm²

• 324 cm²

• 486 cm²

• 729 cm²

Answer explanation

Let the edge of the cube = x So, x³ = 729 i.e., x = ∛729 = 9 cm Total surface area of cube = 6(side)² = 6(9)² = 6(81) = 486 cm² So, option 3 is correct.

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What will be the change in the volume of a cube when its side becomes 1/10 times the original side?

• Volume becomes 1/10 times

• Volume becomes 1/100 times

• Volume becomes 1/1000 times

• Volume becomes 1000 times

Answer explanation

Let the original side of a cube = x Volume of the cube = x³ Now, let the side of the cube become 1/10 times the original side, i.e., side of the new cube = x/10 Volume of the new cube = (x/10)³ = x³/1000 Ratio of volume of new cube to the volume of original cube: Volume of new cube/Volume of original cube = (x³/1000) / (x³) = 1/1000 i.e., Volume of new cube = Volume of original cube/1000 Therefore, when the side of a cube becomes 1/10 times the original side, then Volume becomes 1/1000 times So, option 3 is correct.

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How many cubes each of volume 9 cm³ are required to fill a cubical container of side 18 cm?

• 648

• 72

• 36

• 4

Answer explanation

Volume of cubical container = l³ = 18³ = 5832 cm³ Volume of each small cube = 9 cm³ Number of boxes of volume 9 cm³ that can be accomodated in the container = 5832 cm³ / 9 cm³ = 648 So, Option 1 is correct.

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Three cubes of metal whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. The edge of the new cube is _______.

• 18 cm

• 12 cm

• 6 cm

• 10 cm

Answer explanation

Volume of cube 1 = (3 cm)³ = 27 cm³ Volume of cube 2 = (4 cm)³ = 64 cm³ Volume of cube 3 = (5 cm)³ = 125 cm³ Volume of the new cube = Volume of all three cubes = 27 cm³ + 64 cm³ + 125 cm³ = 216 cm³ Side of new cube = ∛Volume of new cube = ∛216 = 6 cm So, option 3 is correct.

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A cuboid is of dimensions 1.2 m × 1.08 m × 0.6 m. How many small cubes with side 12 cm can be placed in the given cuboid?

• 450

• 1728

• 5400

• 64800

Answer explanation

Volume of the cuboid = Length × breadth × Height = 1.2 m × 1.08 m × 0.60 m = 0.7776 m³ Volume of a small cube = side³ = (12 cm)³ = (0.12 m)³ = 0.001728 m³ Number of required small cubes = Volume of the cuboid/Volume of a small cube = 0.7776 m³/ 0.001728 m³ = 450 So, option 1 is correct.

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