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.