Question

A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ​ft, its width is 7 ​ft, and its surface area is 500 ft2. ​(In the​ figure, h=height. Assume that the given surface area includes that of the top lid of the​ box.)

Answer 1

Explanation:

The surface area of a rectangular box can be calculated as follows:

Surface area = 2lw + 2lh + 2wh

Where l is the length, w is the width, and h is the height.

We are given the surface area (500 ft2) and the length and width (16 ft and 7 ft respectively), so we can use these values to solve for the height:

500 = 2 * 16 * 7 + 2 * 16 * h + 2 * 7 * h

500 = 224 + 32h + 14h

500 = 238h + 224

276 = 238h

h = 276 / 238

h = 1.16 ft

So the height of the box is approximately 1.16 feet.