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 general equation:
by Ady TZIDON)
Nobody cares about the area of the base which is a simple circle of radius b. It is the area of the rest that counts. If the cone were not truncated and had height H, this area would be pi*b*H. Because it is truncated, we need to subtract pi*a*h' where h' is the height of the cone that was cut off in the trucation. Aside from justifying the pi*b*H formula, the problem is to find h' (hence H also) in terms of h, and this can be readily done using similar triangles. Your formulas are way different from what is correct.
(Added in later edit: Sorry. I was a bit confused. Your formulas are correct according to "Handbook of Mathematical Formulas and Integrals, 2nd ed." by Alan Jeffrey. The LA formula differs considerably in form from the one involving the given variables a,b, and h that comes out directly using the difference method, but they do give exactly the same result.)
Edited on January 26, 2004, 5:25 pm
Posted by Richard
on 2004-01-24 12:36:19