Given a cone and a sphere , find the area above the cone and under the sphere.
I figure if I convert this into polar coordinates it will simplify the calculations, so I'll have for the radius since . Now for the angles, I'm not 100% sure, but I would imagine that they're in a neighborhood on the xz and yz planes, but if we consider the xy plane then this will just be a circle centered at 0 with radius 1.
I figure I'll have:
but without the values for , I can't continue.
It's supposed to be volume.
I haven gotten to to spherical coordinates yet, is there a way of solving this using polar coordinates.
doing a little more work on this problem, the closest I got was
after substituting into and setting z=0.
although this solution is incorrect it's supposed to be
For volume you need to solve
Here, f and g are your surfaces
(I'm assuming the top half of the sphere)
For the region of integration, we find the intersection
or
(so the region is a circle)
polar coordinates is definitely the way to go
although my answer is different than yours but the same as the triple integral given by Galactus.