Question

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)??

Answer 1

In spherical coordinates the region outside the cone and above the xy plane corresponds to theta (the angle between the z-axis 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)

Answer 2

This is incorrect