Homework 4


Homework 3: Due Friday 2 February, except as noted below

I think most of the integrals will be fairly straightforward to do once you get them set up. However, If you want to use Maple to help you with any of these problems, feel free to do so. For info on how to use Maple, go to http://hornacek.coa.edu/dave/Maple. Be sure to read both the "general Maple advice" and also the answers to Frequently Asked Question #3.


Section 8.1

  1. 1 (5 points)
  2. 3 (15 points)
  3. 5 (15 points)
  4. 8 (15 points)
  5. 15 (15 points)


Volume of a Donut Compute the volume of a solid torus (aka a donut) with inner radius R and outer radius r. Be sure to label r and R on a diagram; there are different ways to define them. For ... um ... more about donuts, check out this web site. (30 points)


Surface Areas and a trip to the Moon In answering the following questions, you should derive any surface area formula you use. I suggest beginning by trying to use integration to derive the formula for the surface area of a sphere. Start this problem this week, but it won't be due until next week. This problem isn't easy. (50 points total)

  1. What fraction of the earth's surface is visible from the moon?
  2. What fraction of the earth's surface is visible if you are 35,000 feet above the surface of the earth?
  3. What fraction of the earth's surface is visible from a satellite orbiting 280 km above the surface of the earth?


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