Question: Let D be the solid region in three dimensional space that lies in the first octant, and is bounded by the paraboloid \(z={{x}^{2}}+{{y}^{2}}\), the plane z = 1 the plane x-z and the plane y-z.

(a) Setup the limits for an iterated integral to evaluate

(b) Setup an iterated integral to evaluate

by first integrating with respect to z. Change the xy integral to polar coordinates.

(c) Evaluate one of these integrals by hand computation.