Find the area of the surface.

Question

The part of the paraboloid
z = x2 + y2
that lies inside the cylinder
x2 + y2 = 4.

Answer 1

In cylindrical coordinates, you have

z = r^2
r = 2

symmetry allows us to say

v = 4∫[0,2]∫[0,π/2] r^2 * r dr dθ
= 4∫[0,2]∫[0,π/2] r^3 dr dθ
= 2π ∫[0,2] r^3 dr
= 2π * 16/4
= 8π

Answer 2

Its wrong Steve

Answer 3

Odd. It agrees with the formula here

http://www.had2know.com/academics/paraboloid-surface-area-volume-calculator.html

Better double-check my numbers.