Problem

15. BOxes A new refrigutator is shipped in a box 34 inches diep, 6f inches high, and $33 \frac{1}{4}$ inches wide. What is the surface anes of the bax in square feet? Round to the nearest square foot. (Hint: $1 \mathrm{ft}^{2}=14 \mathrm{in}^{2}$ )

Answer

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Answer

\(\boxed{83}\) is the surface area of the box in square feet.

Steps

Step 1 :Given that the length of the box is 34 inches, the width is \(33 \frac{1}{4}\) inches, and the height is 6 feet.

Step 2 :First, we need to convert the height from feet to inches. There are 12 inches in a foot, so the height in inches is \(6 \times 12 = 72\) inches.

Step 3 :The surface area of a box (or a rectangular prism) is given by the formula \(2lw + 2lh + 2wh\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Step 4 :Substitute the given values into the formula, we get the surface area in square inches is \(2 \times 34 \times 33.25 + 2 \times 34 \times 72 + 2 \times 33.25 \times 72 = 11945.0\) square inches.

Step 5 :Finally, we need to convert the surface area from square inches to square feet. There are 144 square inches in a square foot, so the surface area in square feet is \(11945.0 \div 144 = 83\) square feet.

Step 6 :\(\boxed{83}\) is the surface area of the box in square feet.

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