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) $15 \mathrm { in }$.
B) $18 \mathrm { in }$.
C) 21 in.
D) $14 \mathrm { in }$.

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 of the box becomes 3 inches. The length and width of the box are reduced by 6 inches each (3 inches from each side). Let $x$ be the side length of the original square sheet. After the cuts, the dimensions of the box are $(x-6)$ inches by $(x-6)$ inches by 3 inches. The volume is given by $V = (x-6)(x-6)(3) = 675$. Simplifying, we get $x^2 - 12x + 36 = 225$, and solving for $x$ gives $x = 15$ inches. Therefore, the length of one side of the open box is 15 inches.

Solve the Problem 15in15 \mathrm { in }15in B) 18in18 \mathrm { in }18in

Solve the Problem $15 \mathrm { in }$
B) $18 \mathrm { in }$