Question

nicole is going to build a large wooden storage box. the box will be in the shape of a rectangular prism, as shown below. she wants to cover all the sides of the box with special wallpaper that costs $2 per square foot. how much will the wallpaper cost in total?

Explanation:

Step1: Find surface - area formula

The surface - area formula of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height. Here, $l = 8$ ft, $w = 6$ ft, and $h = 7$ ft.

Step2: Calculate $lw$, $lh$, and $wh$

$lw=8\times6 = 48$ square feet, $lh = 8\times7=56$ square feet, $wh=6\times7 = 42$ square feet.

Step3: Calculate the sum inside the parentheses

$lw+lh + wh=48 + 56+42=146$ square feet.

Step4: Calculate the surface area

$SA = 2\times146=292$ square feet.

Step5: Calculate the cost

The wallpaper costs $2$ dollars per square foot. So the total cost $C=2\times SA$. Substituting $SA = 292$ square feet, we get $C = 2\times292=\$584$.

Answer:

$584$