Question

donna is going to build some large wooden storage boxes. the boxes are shaped like rectangular prisms, as shown below. she wants to cover all the sides of each box with special wallpaper. if she has a total of 1498 ft² of wallpaper, how many boxes can she cover? 5 ft 7 ft 6 ft \boxed{} boxes

Explanation:

Step1: Calculate surface area of one box

The formula for the surface area \( S \) of a rectangular prism is \( S = 2(lw + lh + wh) \), where \( l = 7 \) ft, \( w = 6 \) ft, \( h = 5 \) ft.
\[

$$\begin{align*} S&=2(7\times6 + 7\times5 + 6\times5)\\ &=2(42 + 35 + 30)\\ &=2(107)\\ & = 214 \text{ square feet} \end{align*}$$

\]

Step2: Find number of boxes

Divide total wallpaper area by surface area of one box. Let \( n \) be the number of boxes. \( n=\frac{1498}{214} \)
\[
n = 7
\]

Answer:

7