# Centroid of a half cone

1. Jan 30, 2008

### wakko101

The question is this: find the centroid of the half-cone
sqrt(x^2 + y^2) <(oet) z <(oet) 1
and x >(oet) 0
(oet being or equal to, I apologize for the lack of sophistocated symbols). I thought I was doing it correctly, but my answers do not match up with those in the book.

I assumed that it would be wise to use cylindrical coordinates which would make r <(oet) 1 and z <(oet) 1. Now, for the limits of integration, I used

0 < r < 1,
-pi/2 < theta < pi/2 and
0 < z < 1.

The mass is the triple integral of [r dr dtheta dz]. And to find the centroid coordinates I take the triple integral of my particular coordinate multiplied by r and over the mass. I'm pretty sure I know how to integrate, so I assume that my mistake was in my limits or perhaps my choice of coordinate system.

Advice please and thank you....

Cheers,
Wakko. =)

2. Jan 30, 2008

### Dick

It doesn't sound like you are doing anything obviously wrong. Maybe you could post your result and let people check it.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook