Constructing a rectangular box Refer to Example. A box with an open top is to be construct...

Constructing a rectangular box Refer to Example. A box with an open top is to be constructed by cutting 3-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 60 in3?

Example Constructing a rectangular box

A box with a square base and no top is to be made from a square piece of tin by cutting out a 3-inch square from each corner and folding up the sides. If the box is to hold 48 in3, what size piece of tin should be used?

SOLUTION We begin by drawing the picture in Figure, letting x denote the unknown length of the side of the piece of tin. Subsequently, each side of the base of the box will have length x – 3 – 3 = x − 6

Since the area of the base of the box is (x − 6)2 and the height is 3, we obtain

Since the box is to hold 48 in3,

We now solve for x:

Consequently