Question

A pizza company is building a rectangular solid box to be able to deliver personal pan pizzas. The pizza company wants the volume of the delivery box to be 280 cubic
inches. The length of the delivery box is 6 inches less than twice the width, and the height is 2 inches less than the width. Determine the width of the delivery box.
A. 7 inches
B. 5 inches
C. 6 inches
D. 8 inches

Answer 1

Here, we are required to determine the width of the delivery box given the dimensions as in the question.

The correct answer is choice A.

The width of the delivery box is ; w = 7.

A rectangular box had the shape of a cuboid.

Volume of a cuboid = Length × width × height

width = w

Length = 2w - 6

height = w - 2

280 = (w) × (2w - 6) × (w - 2)

280 = (2w² - 6w) × (w - 2)

280 = 2w³ - 4w² - 6w² + 12w

280 = 2w³ - 10w² + 12w

2w³ - 10w² + 12w - 280 = 0

Therefore, w³ - 5w² + 6w - 140 = 0

By testing hypothesis at w = 7, i.e (w - 7) is a factor.

The expression cam be factorized as;

(w - 7)(w² +2w + 20) = 0.

Therefore, the only real solution of w is , w = 7.

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