Your physics class decides to perform an experiment on circular waves. First, you make sure the water in the school swimming pool is level with no waves. Next, a volunteer tosses a small marble near the center of the pool. Your teacher tells you the radius in feet, of the outer ripple is given by, where the time in seconds after the marble hits the water given. The area of the circle is given by the function, where is the area in square feet and is the radius in feet.

1. Find a equations for the composite function. ( give the full decimal and leave the answer terms of pi)
2. what is the input and output of the composite function?
3. Find the area of the circle after the marble hits the water.
4. Assume the marble hit exactly in the middle of the pool. The outer ripple takes to reach the side of the pool. Find the area of the circle.
5. Find the length of the short side of the pool, given the seconds in 4.
6. 6. The area of a circle formed by the outer ribble. How long ago did the marble hit the water?