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?

Answer 1

Answer:

They would need approximately 20 gallons of paint for the water tower, so yes, 25 gallons would be enough.

Step-by-step explanation:

In order to find out if there is enough paint for the surface area of the sphere, you need to first find the radius of the object so you can determine the measure of the entire surface area.  Since they give us the volume, we can use that to solve for the radius using the volume formula:  V = πr³  or 66840.28 = πr³.  Using inverse operations, you can first multiply both sides of the equation by the reciprocal of 4/3 or 3/4, then divide by π, this gives you 15,965 = r³.  In order to find 'r', take the cube root of both sides:  ∛15965 = ∛r³  or r ≈ 25.

Now that you know radius = 25, you can use the formula for surface area:  SA = 4πr²  or 4π(25)² ≈ 7850 ft².  Since one gallon of paint covers 400 square feet, we can take our total and divide by 400 to find the number of gallons:  7850 ÷ 400 ≈ 19.6.  In total, we would need 19.6 gallons of paint for the water tower, so if there are 25 gallons available, there is enough.