Question

The number of $4cm$ cubes which can be cut from a solid cube whose edge is $32cm$ is:

• A. $16$
• B. $64$
• C. $256$
• D. $512$

Answer 1

The correct option is D $512$

We know, volume of a cube $V=a^3$, where $a$ is the edge.

Given, edge of smaller cubes $=4cm$.

Then, volume of smaller cube=$(4{)}^3=64c{m}^3$.

Also, edge of larger cube $=32cm$.

Then, volume of the larger cube$=(32{)}^3=32768c{m}^3$.

Since the smaller cube are cut from the larger cubes, the volume of all the smaller cubes is equal to the volume of the larger cube.

That is,

Total number of smaller cubes $\times$ volume of smaller cubes $=$ Volume of larger cube.

$\therefore$ Total no of smaller cubes $=$ Volume of larger cube $÷$ Volume of smaller cube.

$⟹$ Total no. of smaller cube $=\frac{32768}{64}=512$.

Hence, option $D$ is correct.