A hollow plastic ball floats in a tub of jello (the flavor is irrelevant, but I’ll tell you: it’s key lime). The jello sets, and when the ball is removed, the saucer-shaped depression in the jello measures 6cm across and 1cm deep. If the density of the plastic is twice that of jello, what is the average thickness of the plastic shell?

(In reply to re: solution by Charlie)

Since this is a Calculus question, if we did not use the pre-built formula for the cap of a sphere, we could have gotten that volume from:

∫{4 to 5} π(5²-x²)dx

as we need to integrate π(radius)² where the square of this radius is 5²-x².

This comes out to π[25x - x³/3] evaluated from 4 to 5, which comes out to the same 14π/3.

Posted by Charlie on 2003-04-04 11:24:18