I am trying to understand this example of finding the center of mass of a uniform solid cone.(adsbygoogle = window.adsbygoogle || []).push({});

please refer to the attached figure. We know for obvious reasons that the center of mass will be on the z-axis. I will be referring to the integral that my book used to find the center of mass which is (using the letter S for the integral sign)

R= (1/M) Srdm = (1/M) S krdV

whereRis the position vector, M is the total mass, dm is the element of mass, k is the density, and dV denotes the element of volume.

so for this problem, we have

Z = k/M S z dx dy dz (again, S z dx dy dz means the integral of z dx dy dz)

my first question is how do you evaluate this integral?

thanks

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# Finding the center of mass of a cone

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