Question

A box with no top is being made out of a 20 cm by 30 cm piece of cardboard by cutting equal squares of side length x from the corners and folding up the sides. Determine an algebraic model for the volume of the box. Use your model to determine the volume if the side length of each square is 6 cm.

Answer 1

Given:

length of the sides of the box = x

A diagram of the required box is shown below:

Since the box is made up of a square of side x, the algebraic model for the volume of the box is:

`Volume\text{ = x}^3`

When the side lengths of each square is 6cm, the volume is:

`\begin{gathered} Volume\text{ = 6}^3 \\ =\text{ 216 cm}^3 \end{gathered}`

Answer Summary:

`\begin{gathered} Algebraic\text{ model} \\ Volume\text{ = x}^3 \\ When\text{ x =6} \\ Volume\text{ = 216 cm}^3 \end{gathered}`