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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 -

    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)

  • math -

    This is incorrect

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