Solve the problem.
-A machine produces open boxes using square sheets of plastic. The machine cuts equal-sized squares measuring 4 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by Turning up the sides. If each box must have a volume of 1600 cubic inches, find the length of one side of the Open box.
A)19 in.
B)24 in.
C)28 in.
D)20 in.

Question

Quizplus · Accepted Answer

After cutting out the squares from each corner, the dimensions of the base of the box become (x - 2*4) by (x - 2*4), where x is the original side length of the square sheet. The height of the box is 4 inches (the size of the cut-out square). The volume of the box is given by V = lwh, where l and w are the length and width of the base, and h is the height. Substituting the given volume (1600 cubic inches) and the expressions for l, w, and h, we get 1600 = (x - 8)(x - 8)(4). Simplifying, we find x - 8 = 20, so x = 28. However, the question asks for the length of one side of the open box, which is the length of the base, or x - 8, which equals 20 inches.

Solve the Problem. -A Machine Produces Open Boxes Using Square Sheets of Plastic