Question

Yes another nice problem (attached)

Answer 1

solving both equations gives the region :
x^2 + y^2 + z^2 = 9
z = 7 - x^-y^2

7-z + z^2 = 9
z = 2

Answer 2

\(x = r\cos\theta\)
\(y = r\sin\theta\)

sphere : \(z = \sqrt{9 - r^2}\)
paraboloid : \(z = 7-r^2 \)