14.5 Surface Area The equations for these surfaces can be found at

1 4.5 Surface Area

Recall from Calc BC If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: We need to get dx out from under the radical. Length of Curve (Cartesian)Lengths of Curves:

This formula will be proven at the end of the slide show

Example 1 Find the surface area of the portion of the plane z = 2 – x – y that lies above the circle in the first quadrant.

Example 1 Solution

Example 4 Find the surface area of the portion of the hemisphere that lies above region R bounded by the circle

Example 4 solution

Example 4 solution slide 2

A math professor is one who talks in someone else's sleep.

Proof of surface area formula slide 1

Diagrams for surface area formula