# Find the volume of the solid region given some constraints.

Hi I'm having trouble with this homework question:

"Using spherical coordinates, find the volume of the solid region that lies inside the sphere of radius $R = 3$, under the cone given by $ϕ = π/ 3$ , and above the $xy$-plane."

So as said in the question I used spherical coordinates.

Imagining this I think that the volume $V$ is given by:

$\int_0^{2\pi}\int_{\pi/3}^{\pi/2}\int_0^3r^2sin(\phi)drd\phi d\theta$

I followed this through and got $9\pi$ im not sure this is right.

Is my method along the right lines or am I completely off?

Any help would be appreciated, thanks.

• Why are you limiting theta that way? If you do that, then you will get the volume in the first octant. – Doug M May 2 '17 at 18:56
• thanks i don't know how i missed that ill change it to 2$\pi$ and run it through again – Thomas May 2 '17 at 18:59