Question

A cube is cut into x smaller cubes each of volume 8$c{m}^3$. If volume of the entire cube is 512 $c{m}^3$, then find the value of 'x'.

• A. 16
• B. 96
• C. 64
• D. 32

Answer 1

The correct option is C

64

Given, volume of entire cube = 512$c{m}^3$ and the cube is cut into $x$ smaller cubes of volumes 8$c{m}^3$

Implies, there is shape conversion, but the volume remains same.
$\therefore \text{volume of entire cube =}x\times \text{volume of one smaller cube}$

$x=\frac{\text{volume of entire cube}}{\text{volume of 1 smaller cube}}$

$=\frac{512}{8}=64$

Therefore, the entire cube is cut into 64 smaller cubes.