14.5 Surface Area

The equations for these surfaces can be found at http://virtualmathmuseum.org/Surface/gallery_o.html#PseudosphericalSurfaces

14.5 Surface Area

Recall from Calc BCIf we want to approximate the length of a curve, over a short distance we could measure a straight line.

ds

dx

dy

By the pythagorean theorem:

2 2 2ds dx dy

2 2ds dx dy

2 2ds dx dy We need to get dx out from under the radical.

2 22

2 2

dx dyS dx

dx dx

2

21 dy

L dxdx

2

1 b

a

dyL dx

dx

Length of Curve (Cartesian)

Lengths of Curves:

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

Example 1Find 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