If you have a truncated cone such that its upper base has a radius of a and the radius of its [larger] lower base is b, and a height h (between bases), how could you figure out its surface area using geometric reasoning?

(In reply to re(2): general equation: by Jils)

The problem asks "how could you figure out its surface area using geometric reasoning?" Ady's formulas are correct, but where is the geometric reasoning? Where is there any reasoning? All I see is a set of formulas without any explanation. Developing the surface of the cone is geometric, I contend, and so is finding the untruncated height by similar triangles. Ady's formula for the nontrivial part of the surface area is very nice and succinct, and not easy to algebraically deduce from the difference formula that I gave, but it can be found in handbooks such as the one by Alan Jeffrey. But without the geometric explanation, it doesn't solve the stated problem.

Posted by Richard on 2004-01-26 17:10:51