How much paint is needed for truncated cone tower?

[miss_sana]

Homework Statement

So there's about 4 problems that iI just don't understand. The first one is called H20 in the S-K-Y.
there's a drawing and it kind of looks like a graduated cylinder with a circle on top. It says the spherical top holds a little over 54,000 gallons of water, the base of the top is 60 feet above the ground and the diameter of the suporting column is one-third the radius of the sphere. The base of the supporting column flares out like a cone so that the diameter of the bottom is equal to the radius of the sphere; this bottom section is 15 feet tall. LIkewise, the connection between the support and the spehere flares out to a diameter equal to two-thirds the radius of the sphere and is 10 ft tall.
The paint must be applied to an average thickness of .16 cm over the entire structure. I need to calculate how much paint will be needed to paint the tower based on the details given.

Homework Equations

The Attempt at a Solution

now i know its a surface area problem, and I already converted the gallons into feet, and found that the radius of the circle is 12 ft long. Also, I know that the surface area of what would be the circle is 576pi, but the thing is, it's not whole because it's connected to the supporting column. if anyone could help, that'd be great! =)

 

[HallsofIvy]

I take it you mean "sphere" rather than circle. The base sounds like a truncated cone. You can find a formula for its surface area here:
http://pagesperso-orange.fr/jean-paul.davalan/calc/cone/cone-en.html