# Homework Help: Finding the Mass of a Solid in 3d

1. Nov 25, 2011

### c.dube

1. The problem statement, all variables and given/known data
Find the mass of the solid bounded by the cylinder $x^2+y^2=2x$ and the cone $z^2=x^2+y^2$ if the density is $\delta = \sqrt{x^2+y^2}$

[b2. The attempt at a solution[/b]
I had some trouble looking at how to set up the limits on this integral. What I came up with was:
$2 \int_0^2 \int_0^{\sqrt{2x^2+2x}} \int_0^{\sqrt{x^2+y^2}} \sqrt{x^2+y^2} dzdydx$
$= 2 \int_0^2 x^2\sqrt{x^2+y^2} + ((\sqrt{x^2+y^2})^3)/3 dx$
And this is just an ugly integral. I tried doing it in cylindrical coordinates but it wasn't working out terribly well that way either. Any hints? Thanks!

2. Nov 25, 2011

### c.dube

Nevermind, I got an answer. Can anyone confirm $6\pi$?