Q15. - Algebra 1

Question

BOXES A new refrigerator is shipped in a box 34 inches deep, 66 inches high, and $33\frac{1}{4}$ inches wide. What is the surface area of the box in square feet? Round to the nearest square foot. (Hint: $1 {\mathrm{ft}}^2=144 {\mathrm{in}}^2$)

Step-by-Step Solution

Answer

The surface area of the box is 39 square feet.

Step 1. State the formula.

The formula for surface area of a rectangular prism is $S=lw+wh+hl$, where S is the surface area, l is the length, w is the width and h is the height of the rectangular prism.

Step 2. List the given data.

The box is a rectangular prism of length 34 in, width $33\frac{1}{4}\mathrm{in}.$ and height 66 in.

Then, $l=34\mathrm{in}.$, $w=33\frac{1}{4}\mathrm{in}.$ and $h=66\mathrm{in}.$

Step 3. Calculate the surface area.

Put $l=34$, $w=33\frac{1}{4}$ and $h=66$ in $S=lw+wh+hl$ to get,

$$\begin{gathered} S=\left(34\right)\left(33\frac{1}{4}\right)+\left(33\frac{1}{4}\right)\left(66\right)+\left(66\right)\left(34\right) \\ =\left(34\right)\left(\frac{133}{4}\right)+\left(\frac{133}{4}\right)\left(66\right)+2244 \\ =1130.5+2194.5+2244 \\ =5569 \end{gathered}$$

So, $S=5569$.

Step 4. Determine the unit.

Since the unit of length, width and height are all given as inches, the unit of the surface area must be square inches.

 

So, the surface area of the box is 5569 square inches.

Step 5. Unit conversion.

Now,

$$\begin{gathered} 1{\mathrm{ft}}^2=144{\mathrm{in}}^2 \\ 1{\mathrm{in}}^2=\frac{1}{144}{\mathrm{ft}}^2 \\ 5569{\mathrm{in}}^2=\frac{5569}{144}{\mathrm{ft}}^2 \\ =38.67{\mathrm{ft}}^2\left(\mathrm{roundedto}2\mathrm{decimalplaces}\right) \end{gathered}$$

So, the surface area of the box is approximately 38.67 square feet. Rounding to the nearest square foot, the surface area of the box is 39 square feet.