"The Water Tower" review problem: solids of revolution, applications of integrals, and related rates.

1. The Ellipsoid
Water Tower
Problem ...
... this is how
you'll feel when
you get it.
Smiley Face Water Tower
by flickr user jenniferrt66

2. The town of Calcuville has a water tower whose tank is a circular
ellipsoid, formed by rotating an ellipse around its minor axis. The
tank is 20 feet tall and 50 feet wide.
(a) If there are 7.46 gallons of water per cubic foot, what is the
capacity of the tank to the nearest 1000 gallons?
(b) Calcuville imposes water rationing regulations whenever the
tank is only one quarter full. How deep is the water in the tank
when water rationing becomes necessary?
(c) During peak usage, 5000 gallons of water are used per hour.
How fast is the water level dropping if it is 12 feet deep when
peak usage begins?