An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from?

Question

an open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from each corner and turning up the edges. If the box is to hold 294 cubic inches, what should be the dimensions of the sheet metal?

19 by 19

15 by 15

12 by 12

8 by 8

or none of the above

Answer 1

A.

one side of the box is 6 the other two are equal. so 6x^2 = 294

x^2 = 49

x = 7

one side of the square is 6 + 6 + 7 = 19

Answer 2

When you fold up the sides, the height is going to be 6 inches.  If the volume is going to be 294, we can divide by the height to get the length times width.

294/6=49

Each remaining side is 7 inches

Each original side is 6 inches (cut away) plus 7 inches (left behind) plus 6 inches (cut away), or 19 inches

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