Homework Help?

Question

I need help finding the center of mass of a "conehead" the object is actually two objects put together.
1) A cone
2) A hemishepre

I know that the center of mass of a cone is: 3/4H
and that the center of mass of a hemisphere is: 3/8R

I need help combing these two formulas so that I may find the center of mass of a conehead.

Answer 1

Taking y positive towards the cone from the junction of the two,
y = (3/4)(1/3)πR^2H^2 - (3/8)(4/3)πR^4)/((1/3)πR^2H + (4/3)πR^3)
y = (1/4)πR^2H^2 - (1/2)πR^4)/((1/3)πR^2H + (4/3)πR^3)
y = (1/2)πR^2[(1/2)H^2 - R^2)]/[(1/3)πR^2(H + 4R)]
y = (3/2)[(1/2)H^2 - R^2)]/(H + 4R)
y = (3/4)[H^2 - 2R^2)]/(H + 4R)