Question

Find the area of the surface.
The part of the paraboloid
z = x2 + y2
that lies inside the cylinder
x2 + y2 = 4.
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
Its wrong Steve
Odd. It agrees with the formula here

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

Better double-check my numbers.

Related Questions

Evaluate the surface integral. double integral ydS S is the part of the paraboloid y = x2... Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2z2i + y2z2j + xyzk, S is the part... Find the surface area of the portion of the paraboloid z = 4 - 𝑥^2 -𝑦^2 that lies above the xy- p... Question: Find the surface area of the portion of the sphere x^2 + y^2 +z^2 = 4 that lies inside...