Question: (a) Sketch the solid region contained within the sphere \({{x}^{2}}+{{y}^{2}}+{{z}^{2}}=16\) and outside of the cone \(z=4-\sqrt{{{x}^{2}}+{{y}^{2}}}\)

(b) Clearly identifying the limits of integration (using spherical coordinates) set up the iterated triple integral which would give the volume of the volume bounded by the above. Do not evaluate the integral.

(c) Using Pappus theorem to compute the volume