(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Centroid of cylindrical cone

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