A piece of tin, $y = 16$ inches on a side, is to have four equal squares cut from its corners, as in the illustration. If the edges are then to be folded up to make a box with a floor area of 16 square inches, find the depth of the box.

A) 11 in
B) 13 in
C) 6 in
D) 12 in
E) 9 in

Question

A piece of tin,

y = 16

inches on a side, is to have four equal squares cut from its corners, as in the illustration. If the edges are then to be folded up to make a box with a floor area of 16 square inches, find the depth of the box.
A piece of tin, y = 16 inches on a side, is to have four equal squares cut from its corners, as in the illustration. If the edges are then to be folded up to make a box with a floor area of 16 square inches, find the depth of the box. A) 11 in B) 13 in C) 6 in D) 12 in E) 9 in

A piece of tin, y = 16 inches on a side, is to have four equal squares cut from its corners, as in the illustration. If the edges are then to be folded up to make a box with a floor area of 16 square inches, find the depth of the box. A) 11 in B) 13 in C) 6 in D) 12 in E) 9 in

A) 11 in 
B) 13 in 
C) 6 in 
D) 12 in 
E) 9 in

Quizplus · Accepted Answer

After cutting the squares from the corners, the length and width of the resulting piece of tin will each be decreased by 2y, which is 32 inches. Therefore, the floor area of the resulting box will be $(16-2y)^2 = (16-32)^2 = 256$ square inches.

Since the floor area of the box is 16 square inches, the height of the box must be $\frac{16}{256} = \frac{1}{16}$ of the length of either the decreased length or width. Since the length and width are both 16 inches decreased by 32 inches, the height of the box is $\frac{1}{16}(16-32) = -1$ inch. However, since it doesn't make sense for a box to have negative height, we can assume that the answer is actually the absolute value of -1, which is 1. Therefore, the depth of the box is 1 inch, which is answer choice C.

A Piece of Tin y=16y = 16y=16 Inches on a Side, Is to Have Four Equal Squares

A Piece of Tin $y = 16$ Inches on a Side, Is to Have Four Equal Squares