When the flag below is rotated it has a volume of $| \frac { 243 } { 2 } \pi |$ un³.

1. Describe the resultant three-dimensional figure.

   Hint (a):

   Use the eTool below to visualize the rotating flag.
   Click the link at right for the full version of the eTool: Calc 1-60 HW eTool

2. What is the value of $d$?

   Hint (b):

   $\frac{243}{2}\pi =\frac{4}{3}\pi r^{3}$

   More Help (b):

   $r=\frac{1}{2}d$

3. If the diagram was rotated $90°$ and the flag was then rotated about a horizontal pole, would the volume change?

   Hint (c):

   Build a model by taping a paper flag to a pencil. Try holding the pencil in different positions. Does the size or shape of the resultant solid change when the pencil is held horizontally vs. vertically?