Question

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

• A. 36
• B. 232
• C. 216
• D. 484

Answer 1

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, $n=\frac{\text{volume of larger cube}}{\text{volume of a smaller cube}}$

We know, volume of a cube of side 'a' is $a^3$.

$\Rightarrow n=\frac{18\times 18\times 18}{3\times 3\times 3}\therefore n=216$

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