Question

A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 15 ​ft, its width is 9 ft, and its surface area is 606 ft squared (In the​ figure, Assume that the given surface area includes that of the top lid of the​ box.)

Answer 1

The surface area of a rectangular box can be found by adding the area of each face:

2lw + 2lh + 2wh = 606
where l is the length, w is the width, and h is the height.

Given that the length is 15 ft and the width is 9 ft, we can substitute these values into the equation:

2 * 15 * 9 + 2 * 15 * h + 2 * 9 * h = 606
270 + 30h + 18h = 606
48h = 336

Dividing both sides of the equation by 48:

h = 7

So the height of the box is 7 ft.