Cylindrical coordinates?

Question

Use cylindrical coordinates to find volume of the solid bounded by the paraboloid z=x^2+y^2 and the plane z=4.

Answer 1

A point in space has cylindrical coordinates (r,phi ,z) where r and phi are the polar coordinates of the proyection of the point on the xy plane
so z= r^2 and must calculate the integral of pir^2 dz = pi *zdz
between 0 and 4 which yields

pi/2(4^2-0^2)= 8*pi