ok so we have
is the region that we want.
so we convert to spherical coordinates.
it is obvious that and
to find the values for we have
which is
so we have
and i am sure that you can solve it from here.
Find the volume of the solid above the cone and below the sphere
Obviously use polar coordinates here.
So the two equations are and .
I'm trying to draw the region of integration in the x-y plane and getting stuck. I think the cone comes down to a single point at (0,0), so maybe that can be disregarded. The sphere has a projection of a unit circle. So is the region of integration the unit circle?
Also what are the bounds for the integral?
That spherical method is just what I was gonna post. That's what I arrived at also.
Oh well, here's another way, but equivalent in rectangular.
Now, do it in cylindrical coordinates.
Thanks for the fix PH. Everytime I tried to edit last night I kept getting a "this page can't be displayed" window, so I just gave up.