1. The problem statement, all variables and given/known data Determine the centroid of volume for a right circular cone with base diameter of 100mm and an altitude of 200mm. 2. Relevant equations I know that if the my xy-plane is parallel to the base of the cylindrical cone then the x and y coordinates of the centroid must be zero and therefore I only need to find the z coordinate of the centroid. The equation I am using is [tex]z_c = \frac{1}{M} \int_{body} z dm[/tex] where M is the total mass and [tex]dm = \rho dV[/tex] 3. The attempt at a solution I am trying to use cylindrical coordinates but I think my limits of integration are incorrect. I have tried to solve the integral above with the following limits. [tex]0<\theta<2\pi [/tex] [tex]0<r<50 [/tex] [tex]0<z<(200-r/4)[/tex] I'm not sure if the limits for the z coordinate is correct. Am I on the right path?
Well, I wouldn't worry with polar coordinates, because you are dealing with basically a stack of disks aren't you? They are each have a weight of ρ*πr² Exploit then the fact that r is a function of z, and your integral should be pretty straight forward shouldn't it?
Thank you. I was essentially doing the right thing on my first try before I changed everything, but I made an algebra mistake when trying to use cylindrical coordinates. Thanks for the short cut ... less room for stupid mistakes.