Choose the one alternative that best completes the statement or answers the question.
-A rectangular piece of tin has an area of 703 square inches. A square of 4 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 1,276 cubic inches, what were the
Original dimensions of the piece of tin?
A) 15 in. by 33 in.
B) 19 in. by 37 in.
C) 11 in. by 25 in.
D) 23 in. by 41 in.

Question

Quizplus · Accepted Answer

After cutting 4-inch squares from each corner and folding up the sides to form a box, the original length and width of the tin are reduced by 8 inches each (4 inches from each side). Let the original dimensions be $l$ and $w$. The volume of the box is given by $V = (l - 8)(w - 8) \times 4$, since the height of the box is 4 inches. Given $V = 1276$ and the area of the original piece of tin is $703$ square inches ($lw = 703$), we can solve these equations simultaneously. Among the given options, only the dimensions $19 \times 37$ satisfy both the area of the original piece of tin and the volume of the box formed.

Choose the One Alternative That Best Completes the Statement or Answers