Guys I am really having trouble constraining the region between these three surfaces. I am imagining a sort of "Dome", or a "muffin head" sort of shape. Is this correct ? Anyway, I need to be able to write the following volume integral in rectangular, cylindrical and spherical coordinates:
Consider the region that is between $x^2 + y^2 + z^2 = 1$, $x^2 + y^2 + z^2 = 9$, and finally above the upper nappe of the cone $z^2 = 3(x^2 + y ^2)$
upon further consideration, does the smaller sphere even matter ? wouldn't it just represent a hole in the larger sphere, an area im not even worried about finding the volume of ?
Anyway, thanks for looking!