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Let S1: x^2+y^2=4 and S2: z=−√(x^2+y^2) be two surfaces in space. (a) [2] Graph these two...

Let S1: x^2+y^2=4 and S2: z=−√(x^2+y^2) be two surfaces in space.

(a) [2] Graph these two surfaces.

(b) [4] Find equations of S1 and S2 in spherical coordinate system .

(c) [4] Find the intersection of S1 and S2 in this (spherical) coordinate system.

(d) [5] SET UP but DO NOT EVALUATE the triple integral in spherical coordinate system to evaluate the volume which is above the xy -plane, outside of S1 and inside of S2 .

(Bonus) [2] Can you geometrically say what would be the volume above?

(You score 0 if solve parts b, c, and d in other coordinate systems.)

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