A solid cube of side 12 cm is cut into 8 smaller cubes of equal volume. The side of the smaller cube is

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9 cm

3 cm

6 cm

12 cm

answer is B.

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Detailed Solution

Let the side of the smaller cube be x.

It is given that a cube of side 12 cm is cut into 8 smaller cubes of equal volume.

Therefore, the volume of 8 smaller cubes will be equal to the volume of the bigger cube.

It is known that the volume of a cube = a³

The volume of 8 smaller cubes = 8x³

∴ a³= 8x³

⇒ (12)³ = 8x³

⇒ x³ = 1728/8

⇒ x³ = 216

⇒ x = 6 cm

Therefore, the side of the smaller cubes will be 6 cm.

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