Posted by alana on Thursday, April 9, 2009 at 3:32pm.
how do you find the volume of the solid that lies within the sphere
x^2+y^2+z^2=9
above the xy plane, and outside the cone
z=2*sqrt(x^2+y^2)??

math  Count Iblis, Thursday, April 9, 2009 at 5:16pm
In spherical coordinates the region outside the cone and above the xy plane corresponds to theta (the angle between the zaxis and the position vector)between
arctan(1/2) and pi/2.
So, the volume is:
Integral over phi from 0 to 2pi
Integral over theta from atn(1/2) to pi/2
Integral over r from 0 to 3
dr dtheta dphi r^2 sin(theta)

math  Ellen, Tuesday, April 17, 2012 at 6:34pm
This is incorrect
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