# Thread: Cylindrical and Spherical coords volume

1. ## Spherical coords volume

Hello,

I keep getting this volume wrong by a factor of 4... I keep ending up with $\displaystyle 16 \ pi \sqrt{3}$ instead of $\displaystyle 4\pi \sqrt{3}$. Could someone please tell me what's wrong in my integral?

Question is: Find the volume that is inside $\displaystyle x^2+y^2+z^2=4$ but outside $\displaystyle x^2+y^2=1$.

My integral is $\displaystyle \int_0^{2\pi} \int_{\frac{\pi}{6}}^{\frac{5\pi}{6}} \int_{\frac{1}{\sin \phi}}^2 \rho^2 \sin \phi d \phi d \rho d \theta$.

Thanks

EDIT: I've figured out how to do this problem... Took quite a bit though... So I don't need help on this problem anymore

2. I can do this using cylindrical shells and cylindrical coordinates but I cannot doing it using spherical coordinate (which the method requested by the question).

I really cannot see how my limits are wrong, especially given that these two methods do work. Could someone please point out why my method in the first post using spherical coordinates yields the wrong answer? It's driving me crazy.

Thanks heaps