The z com of the entire ice cream cone, the base being an inverted right circular cone, the top a hemisphere. Equal density throughout. Must solve using integrals and density relationship.
The z com of the top hemisphere (ice cream) is equal to 3/8 R
The z com of the lower section (cone) is equal to h/4
The Attempt at a Solution
m = density * volume
mt/mb = (2/3*PI*R^3) / (1/3*PI*R^2*h) = 2R/h
zcom = 1/M summation m*z
(h/2R) = summ (2/3*PI*R^3) * (3/8*R) + (1/3*PI*R^2*h) * (h/4)
To be honest, I have no clue what I am doing. I know I need to some how come up with a way, using the density relationship, to set up an integral and solve the total z com of the two solid components. I'm not sure if what I did above is on the right track. Please Help!