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Question

How many solid cubes of 3 cm edge can be cut out of a solid cube of 18 cm edge?

A
36
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B
232
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C
216
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D
484
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Solution

The correct option is C 216
Given, edge length of the larger cube = 18 cm
and, edge length of the smaller cube = 3 cm

The volume is the space occupied by a body .So cutting an object does not change its volume.
So, number of smaller cubes × volume of each smaller cube = volume of the larger cube
Let 'n' be the number of smaller cubes.
Then, n=volume of larger cubevolume of a smaller cube

We know, volume of a cube of side 'a' is a3.

n=18×18×183×3×3n=216

So, the number of solid cubes of 3 cm that can be cut out of a solid cube of 18 cm is 216.

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