Suppose That an Empty Circular Wading Pool Has a Radius $g$

Essay

Suppose that an empty circular wading pool has a radius of 9 feet. During a storm, rain falling at a rate of 0.5 inch per hour begins to fill the pool. A small drain at the bottom of the pool is capable of draining 20 gallons of water per hour.
(a) Determine the number of cubic inches of water falling into the pool in one hour. (Hint: Each hour a layer of water 0.5 inch thick falls into the pool.)
(b) One gallon of water equals about 231 cubic inches. Write a formula for a function $g$ that computes the gallons of water landing in the pool in $x$ hours.
(c) How many gallons of water land in the pool during a 2.5 hour storm?
(d) Will the drain be able to keep up with the rainfall? If not, how many such drains would be needed?