Question

A cube of side $16\text{cm}$ is given. How many cubes of side $4\text{cm}$ each will fit in the given cube?

• A. $16$
• B. $4$
• C. $64$
• D. $254$

Answer 1

The correct option is C $64$

We know the volume of cube of side $a$ is calculated as,

$V={\text{(a)}}^3$



Therefore, the volume of cube of side $16\text{cm}$ is

$\begin{array}{cc}\text{Volume of bigger cube}& =(16{)}^3\\ & =4096\end{array}$

The volume of smaller cube of side $4\text{cm}$ will be

$\begin{array}{cc}\text{Volume of smaller cube}& =(4{)}^3\\ & =64\end{array}$

Now, divide the volume of bigger cube by smaller cube to find the number of smaller cubes that will fit in the bigger cube.

$\begin{array}{cc}\text{Number of cubes required}& =\frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}}\\ & =\frac{4096{\text{cm}}^3}{64{\text{cm}}^3}\\ & =64\end{array}$

Hence, $64$ cubes of side $4\text{cm}$ each will fit in the cube of side $16\text{cm}$.