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

1. Describe the resulting 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):

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

   Math Note (b):

   Prism: $V=Bh$;   Cylinder: $V=\pi r^2h$;   Sphere: $V=\frac{4}{3}πr^3$;  Pyramid: $V=\frac{1}{3}Bh$;  Cone: $V=\frac{1}{3}πr^2h$

3. If the diagram is rotated $90^\circ$ and the flag is then rotated about a horizontal pole, will the volume change?