A draining hemispherical reservoir: Water is flowing at the rate of 6 m3/min from a reservoir shaped like a hemispherical bowl of radius 13 m, shown here in profile. Answer the following questions, given that the volume of water in a hemispherical bowl of radius R is V = (π/3)y2(3R - y) when the water is y meters deep.
a. At what rate is the water level changing when the water is 8 m deep?
b. What is the radius r of the water's surface when the water is y m deep?
c. At what rate is the radius r changing when the water is 8 m deep?