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

Answer:

$s^3$

where s is the edge length of the cube-shaped box

Step-by-step explanation:

Let the edge length of the cube-shaped box=s

The edge length of a cube-shaped crate is the square of the edge length of a cube-shaped box.

• Therefore, edge length of the cube-shaped crate$=s^2$

To determine the number of boxes that can fit in the crate, we first find the volume of the crate and the box.

• Volume of the cube-shaped crate of side length $s^2=(s^2)^3=s^6 cubic units$
• Volume of the cube-shaped box of side length $s=s^3 cubic units$

Therefore, the number of boxes that can fit in the crate

=Volume of Crate divided by Volume of Box

$=\frac{s^6}{s^3}\\=s^{6-3}\\=s^3 boxes$

Therefore, an expression for the number of boxes that can fit in the crate is $s^3$.