Question

The edge of a cube is $20$ cm. How many small cubes of $4$ cm edge can be formed from this cube?

• A. $4$
• B. $32$
• C. $64$
• D. $125$

Answer 1

Answer: (D)

$125$

Give, edge of cube $a=20cm$.

Volume of cube = $a^3={20}^3=8000c{m}^3$.

If cubes of edge [$b=4cm$] ismade from this cube, then

its volume $=4^3=64c{m}^3$.

Let $x$ cubes can be made.

Therefore,

Volume of large cube = $x\times$ Volume of small cube $....[a^3=x{b}^3]$

$\Rightarrow 8000=x\times 64$

$\Rightarrow x=\frac{8000}{64}$

$\Rightarrow x=125$.

Hence, $125$ cube can be made from the large cube of edge $20cm$.

Therefore, option $D$ is correct.