Question

How many solid cubes of 6-cm edge can be cut out of a solid cube of 24-cm edge?

• A. 32
• B. 64
• C. 128
• D. 256

Answer 1

The correct option is B 64

Given,
The edge length of the larger cube is 24 cm.
The edge length of the smaller cube is 6 cm.

Now, the 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 $a^3$.

$\Rightarrow n=\frac{24\times 24\times 24}{6\times 6\times 6}\therefore n=64$

So, the number of solid cubes of 6 cm that can be cut out of a solid cube of 24 cm is 64.