Question

A cube of $18\text{cm}$ is given. How many cubes of $3\text{cm}$ each will fit in the given cube?

• A. $18$
• B. $3$
• C. $27$
• D. $24$

Answer 1

The correct option is C $27$

We know that the volume of cube is calculated as,

$V=a^3$,

where $V$ is the volume of cube and $a$ is its side.

Therefore, the volume of larger cube, i.e., the cube with side $18\text{cm}$ will be,

$\begin{array}{cc}\text{Volume of larger cube}& =(18{)}^3\\ & =5832{\text{cm}}^3\end{array}$

and the volume of smaller cube with side $6\text{cm}$ will be

$\begin{array}{cc}\text{Volume of smaller cube}& =(6{)}^3\\ & =216{\text{cm}}^3\end{array}$

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

$\begin{array}{cc}\text{Number of cubes required}& =\frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}}\\ & =\frac{5832}{216}\\ & =27\end{array}$

Hence, $27$ cubes of side $6\text{cm}$ each will fit in a single cube of side $18\text{cm}$.