Question

Whats the volume of the solid cutted from the sphere defined by x^2 + y^2 + z^2=4 by the cilinder defined by r=2sin theta ?

Answer 1

\[\int\limits_{0}^{\Pi}\int\limits_{0}^{2\sin \theta}\int\limits_{-\sqrt{4-r^2}}^{\sqrt{4-r^2}} r dzdrd \Theta\]

Answer 2

do i got this right?

Answer 3

Ages since I did this stuff:

How about 4 int (-4 to 2sin theta) int (0 to 4-x^2) sqrt(4-x^2-y^2) dxdy.

(maybe).

Answer 4

I guess thats valid too, but i think it might be a shortcut to do this with cilindric coords... im gonna try both anyways. Thank you!