Question

The edge length of a cube-shaped crate is the square of the edge length of a cube-shaped box. Write an expression for the number of boxes that can fit in the crate.

Answer 1

Number boxes fit in crate :

Let $x$ be the length of a cube-shaped box.

So, the length of the cube-shaped crate $=x^2$

The volume of a cube is $V=s^3$.

So, the volume of the box is

$V=x^3$

And the volume of the crate is

$\begin{array}{rcl}V& =& {\left(x^2\right)}^3\\ & \Rightarrow & V=x^6\end{array}$

Now, find the number of boxes that can be fit in the crate as shown:

$$\begin{gathered} \frac{x^6}{x^3}=x^{6-3} \\ =x^3 \end{gathered}$$

Hence, the $x^3$ boxes can fit in the crate.