Question

A cubical box with edge $18cm$ is filled with smaller cubes of edge $3cm$. How many small cubes are there in the box?

• A. $218$ cubes
• B. $296$ cubes
• C. $26$ cubes
• D. $216$ cubes

Answer 1

The correct option is D $216$ cubes

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

Now, edge of the cubical box $=18cm$.

Therefore, Volume of the cubical box $={18}^3=5832c{m}^3$.

Now, edge of the smaller cube $=3cm$.

Therefore, Volume of smaller cube$=3^3=27c{m}^3$.

Then, Number of cubes $\frac{\text{Volume of the cubical box}}{\text{Volume of the smaller cube}}$

$=\frac{5832}{27}=216$ cubes.

Hence, option $D$ is correct.