An agricultural sprinkler distributes water in a circular pattern of radius 100 ft. It supplies water to a depth of e^-r feet per hour at a distance of r feet from the sprinkler.
(a) If 0 < R < 100, what is the total amount of water supplied per hour to the region inside the circle of radius R centered at the sprinkler?
(b) Determine an expression for the average amount of water per hour per square foot supplied to the region inside the circle of radius R.