Question

Use the additivity of moments to find the COM of an ice cream cone consisting of a semicircle of density ρ on top of an equilateral triangle of side 6 and density 5ρ. The diagram given is: http://i47.tinypic.com/mscp0.jpg

Answer 1

First, you want the moment of the semicircle, and then, you want the moment of the equilateral triangle. Treat as point masses subsequently.

Answer 2

The equilateral triangle should be trivial. The semicircle is a more complicated problem and requires either geometry or a nasty trig integral.