next up previous
Next: About this document Up: Scratching the Surface Previous: Background

Exercises

  1. Use Maple to verify that in the special case of a surface . (Hint - define your surface by and let Maple do the hard work.)
  2. Find the surface area of above the rectangle , .
  3. Find the surface area of the part of that lies above z=0. (Hint - parametrize the surface by polar coordinates , or convert the integral in rectangular coordinates to polar coordinates.)
  4. Find the lateral area of a cylinder of radius R and height H using a double integral. Lateral area means that the area of the top and bottom of the cylinder is not included. (Hint - the cylinder is given by the equation , for . A good way to parametrize the surface of the cylinder is .)
  5. Find the surface area of the torus defined parametrically by , , .



William W. Farr
Mon Sep 25 09:30:08 EDT 1995