The Bouncy Kat toys are manufactured using a layering process. The plastic is added to the ball one layer at a time, with the radius of each ball increasing at a
rate of 0.1 inch per second. We have been unable to correctly manage the volume
of plastic flowing into the machine. Assuming the machine produces 100 toys at a
time, what is the appropriate flow rate of the plastic (in cubic inches per second)
when the radius of each toy is 0.5 inch? What should the average flow rate of the
plastic be over each 10-second production cycle?