This applet shows a circle being rotated about it's diameter. The circle will rotate based on the slider a.

First try sliding a by hand. What happens to the circle? Then try turning on the the Trace or clicking the Animate button.

Move the slider for a to manipulate this applet. The following are all based on the variable a: -The radius of the small sphere is a -The radius of the large sphere is 2a -The Volumes and Surface Areas of the spheres are displayed dynamically on the left -Point D is a point (x,y) of (radius, volume) for the small sphere -Point F is a point (x,y) of (radius, surface area) for the small sphere

1) What is the ratio of the volume of the large sphere to the volume of the small sphere when a=1? 2) Does that ratio change when you change a? 3) Compare the traced graphs of Points D and F. What are similarities? Differences?