Solve the problem.
-A machine produces open boxes using square sheets of plastic. The machine cuts equal-sized squares measuring 3 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 675 cubic inches, find the length of one side of
The open box.
A)15 in.
B)18 in.
C)21 in.
D)14 in.

Question

Quizplus · Accepted Answer

The volume of the box is given by the formula V = lwh, where l, w, and h are the length, width, and height of the box, respectively. Since squares of 3 inches are cut from each corner of the square sheet, the height (h) of the box becomes 3 inches. The length and width of the box (l and w) are reduced by 6 inches from the original size of the square sheet (3 inches from each side). Let x be the length of one side of the original square sheet. The volume formula becomes V = (x - 6)(x - 6)(3) = 675. Simplifying, we get (x - 6)^2 = 225, and taking the square root gives x - 6 = 15. Therefore, x = 21 inches. However, the question asks for the length of one side of the open box, which is x - 6 = 21 - 6 = 15 inches.

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