# Parameterizing surface in surface integral problem

## Homework Statement

Find the area of the surface cut from the paraboloid z=2x2+2y2 by the planes z=2 and z=8.

## Homework Equations

Surface area of S= ∫∫ ||Ts×Tt|| ds dt

## The Attempt at a Solution

What I am really having trouble doing in this problem (and in general) is parameterizing the surface in terms of s and t. I think for this surface an accurate parameterization is (s,t,√(2s2+2t2)) but I am not sure. Also, I wouldn't know how the planes cutting the paraboloid would come into play.

Dick
Homework Helper
Why did you put the square root into (s,t,√(2s^2+2t^2)) for a starting point? The planes will define the (s,t) region you will integrate over.

Good question. I seem to have made an error. I was looking at the parameterization of a different paraboloid and must have gotten mixed up.

Dick
Homework Helper
Good question. I seem to have made an error. I was looking at the parameterization of a different paraboloid and must have gotten mixed up.
Ok, so just use (s,t,2s^2+2t^2). Now if z=2, then that means 2s^2+2t^2=2. What kind of curve is that in the (s,t) plane?

A circle of radius 1. When z=8, the curve will be a circle of radius 2. Not sure where to go from here.

Dick