# centroid of cylindrical cone

by zandria
Tags: centroid, cone, cylindrical
 P: 15 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 $$z_c = \frac{1}{M} \int_{body} z dm$$ where M is the total mass and $$dm = \rho dV$$ 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. $$0<\theta<2\pi$$ [tex]0
 HW Helper P: 5,346 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?
 P: 15 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.

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