# Volume between $z = 3\sqrt{x^{2} + y^{2}}$ and $x^{2} + (y-1)^{2} = 1$ and $z = 0$

Find the volume between $z = 3\sqrt{x^{2} + y^{2}}$ and $x^{2} + (y-1)^{2} = 1$ and $z = 0$

I am not sure how to approach finding the limits of integration. Would I need to change coordinate systems?

• Yes that is a good idea. The $f(x^2+y^2)$ term hints that polar coordinates should work. But it is a very good exercise to do it in spherical coordinates as well. – Kuifje Dec 16 '15 at 1:20

## 1 Answer

Hint: what is the projection of the solid in the $xy$ plane? Let $D$ be this zone.

Once you have determined $D$, ask yourself, how does $z$ vary over $D$.