Question

Sam wants to cover a gift box with paper the top of the box is 8in wide and 15in long the box is 12in tall what is the minimum amount of paper Sam will need to cover the entire box?

Answer 1

In order to find the amount of paper that will be needed, we need to calculate the surface area of this rectangular prism.

The faces of this figure are:

- 2 rectangles with dimensions 8 in and 15 in,

- 2 rectangles with dimensions 15 in and 12 in,

- 2 rectangles with dimensions 12 in and 8 in.

Calculating the area of each rectangle, we have:

`\begin{gathered} A_1=8\cdot15=120 \\ A_2=15\cdot12=180 \\ A_3=12\cdot8=96 \end{gathered}`

Now, the surface area is:

`\begin{gathered} S=2A_1+2A_2+2A_3 \\ S=240+360+192 \\ S=792\text{ in}^2 \end{gathered}`

So the amount of paper needed is 792 in².