My question in regard to this problem is that I do
not know where to begin. If you can help me out with it, I'll appreciate
it.
Thank you,
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Well, 12.7 so we're talking spherical coordinates. Inside x^2+y^2+z^2=64 and above the xy-plane says were in the northern hemisphere of a sphere of radius 8. Outside the cone says you have to poke a hole in the top of the cone: the cone is pretty sharp, the radius of the cone is one seventh times the height. This means that the angle phi satisfies tan(phi)=1/7 or phi =~0.14 radians. Thus the limits of integration on theta are 0 to 2pi, on phi from 0.14=arctan(1/7) and on rho from 0 to 8,
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