1. The problem statement, all variables and given/known data The problem is to calculate the volume of the region contained within a sphere and outside a cone in spherical coordinates. Sphere: x2+y2+z2=16 Cone: z=4-√(x2+y2) 2. Relevant equations I am having difficulty converting the equation of the cone into spherical coordinates. Judging by the graph I was able to deduce from the formulas (working in rectangular coordinates), I believe I will need the cone equation as the inside ρ limit. 3. The attempt at a solution Converting the sphere into spherical coordinates: x2+y2+z2=16 ρ2=16 ρ=4 a sphere with radius 4 centered at the origin, which is consistent with my graph. I recognize that the cone is downward opening and peaks at z=0. My attempt to convert the equation was as follows: ρcos[itex]\phi[/itex]=4-√(ρ2sin2[itex]\phi[/itex]cos2θ+ρ2sin2[itex]\phi[/itex]sin2θ) ρcos[itex]\phi[/itex]=4-ρsin[itex]\phi[/itex] ρ(cos[itex]\phi[/itex]+sin[itex]\phi[/itex])=4 I can't figure out how to further simplify this formula. All the examples of cones in spherical coordinates I came across were peaked at the origin and simplified nicely to [itex]\phi[/itex]=(some arbitrary angle), but I couldn't find any that were more complicated. This is my first post so please let me know if I've done anything wrong, and thanks in advance!