Exercises

1. For each function below,
   1. Plot its surface of revolution.
   2. Find the volume of the solid of revolution about the x-axis.
   3. Find the surface area of the surface of revolution about the x-axis.
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2. Now generalize the results from Exercise 1 by taking advantage of Maple's symbolic capabilites and find the volume and surface area for:
   1. about the x-axis
   2. about the x-axis
   3. about the x-axis
   (Your answers in each case may have parameters a and/or h in them. Also, results for parts a and b should already be known to you!)
3. Consider the set of all points satisfying

   

   1. Describe the set of points.
   2. If this curve is rotated about the x-axis, describe the resulting surface and solid of revolution.
   3. What is its surface area?
   4. What is its volume?
   5. Why is the condition important geometrically?