# Oil Storage Quiz Puzzle Answer

An oil storage facility not far from Quiz Master Shop Towers has several spherical 100,000-gallon tanks to store oil (as you would expect :-)). They have just had installed their first spherical 800,000-gallon tank, and they are both excited and concerned.

The excitement is obvious, but the concern comes from the need to paint the new tank. All of the tanks need regular painting to prevent corrosion, and they know that 100 litres of paint is needed to cover the 100,000-gallon tanks, but they are not sure how much paint is needed for the 800,000-gallon tank.

So they came to us, thinking we might be able to help.

How many litres of paint is needed for the 800-gallon tank?

The volume of a sphere is proportional to the cube of its radius, and the bigger tank is eight times the size of the smaller tanks. Eight is two cubed, so the radius of the bigger tank is twice that of the smaller tanks.

However, the surface area of a sphere is proportional to the square of its radius. So doubling the radius quadruples the surface area.

Thus 400 litres of paint is needed.