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  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.
  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. tex2html_wrap_inline219 about the x-axis
    2. tex2html_wrap_inline221 about the x-axis
    3. tex2html_wrap_inline223 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 tex2html_wrap_inline229 important geometrically?

Sean O Anderson
Tue Dec 3 12:06:23 EST 1996