Question

One gallon of paint covers 400 square feet of surface area. A typical spherical water tower holds 66,840.28 cubic feet of water. If a city has 25 gallons of paint available, will there be enough to paint the outside of a typical spherical water tower?

Show work to justify the answer.

Answer 1

Yes. 25 gallons of paint is enough to paint outside of the spherical tower.

Explanation:

One gallon of paint covers Area = 400 square feet

25 gallons of paint can cover Area =400 x 25 = 10000 square feet

Amount(Volume) of water that tower can hold = 66840.28 cubic feet

This means the volume of the spherical tower is 66840.28 cubic feet. Since we have to paint the outside of the tower, we need to find the Surface Area of the tower. Using the volume we can first find the radius of the spherical tower and using the radius we can find the Surface Area.

Volume of sphere =
`(4)/(3)`πr³

`66840.28=(4)/(3)`πr³

Simplifying the equation, we get r:

r = 25.18 feet

Surface Area of sphere = 4πr² = 4π(25.18)² = 7967.48 square feet

The Area we required to paint is 7967.48 square feet which is less than the pain we have 10,000 square feet. Therefore, 25 gallons of paint is enough to paint the outside of a typical spherical water tower.