A horizontal flag is shown below.

1. Imagine rotating the flag about its pole and describe the resulting three-dimensional figure. Draw a picture of this figure on your paper.

   Answer (a):

   Imagine a cylinder with cones carved out of the top and bottom.

2. Calculate the volume of the rotated flag.

   Hint (b):

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

   Steps (b):

   $\text{Volume = cylinder }-2(\text{cone})=\pi r^{2}h-2\left ( \frac{1}{3}\pi r^{2}h \right )$

   Answer (b):

   $48\pi\text{ units}^{3}$