Question

A window box for flowers is a rectangular prism

with an open top, as shown. Tyrell wants to coat
the inside and outside of the box with a special
varnish that will protect it from the effects of
water, cold, and harsh weather. The varnish
comes in cans that can cover 500 square inches.
How many cans of the varnish should Tyrell buy?
Explain your answer.

Answer 1

To find the surface area of the window box, we need to add up the areas of all six faces. Since the box has an open top, we don't need to worry about coating the inside of the top face.

The box has two identical rectangular faces (the front and back) with dimensions 24 inches by 12 inches, so each face has an area of 24 x 12 = 288 square inches.

The box has two identical rectangular faces (the sides) with dimensions 18 inches by 12 inches, so each face has an area of 18 x 12 = 216 square inches.

The box has a rectangular bottom face with dimensions 24 inches by 18 inches, so it has an area of 24 x 18 = 432 square inches.

Adding up all six faces, we get a total surface area of 2(288) + 2(216) + 432 = 1440 square inches.

Since each can of varnish covers 500 square inches, we need to divide the total surface area by 500 to find the number of cans needed:

1440 / 500 = 2.88

We can't buy a fraction of a can, so we need to round up to the nearest whole number. Therefore, Tyrell should buy 3 cans of the varnish to coat both the inside and outside of the window box.