Solve the problem.
-An open box is to be constructed from a square sheet of plastic by removing a square of side 4 inches from each corner, and then turning up the sides. If the box must have a volume of 1,600 cubic inches, find the length of one
Side of the open box.
A) 20 in.
B) 19 in.
C) 24 in.
D) 28 in.

Question

Quizplus · Accepted Answer

The original square sheet's side length is x inches. After removing 4-inch squares from each corner and folding up the sides, the base of the box becomes (x - 2*4) inches by (x - 2*4) inches, or (x - 8) inches on each side. The height of the box is 4 inches (the side of the removed squares). The volume of the box is given by the formula for the volume of a rectangular prism, V = lwh, where l = length, w = width, and h = height. Substituting the given values, we have 1600 = (x - 8)(x - 8)(4). Simplifying, 1600 = 4(x - 8)^2, or 400 = (x - 8)^2. Taking the square root of both sides gives x - 8 = 20, so x = 28 inches. Therefore, the length of one side of the original square sheet of plastic is 28 inches.

Solve the Problem. -An Open Box Is to Be Constructed from a Square