Centroid of half-cone with sqrt(x^2+y^2)≤z≤1, x≥0

[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. =)

 

[Dick]

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