Calculus problem optimiizing

Historically, there have been several major oil spills. Wild life suffers greatly and the ecosystem is thrown into disarray. Time is of ultimate concern and goals are to stop the flow of oil from the tanker and confine the oil spill using floating containment booms as quickly as possible. An old taker has gone aground on a reef and has punctured the oil tank. Oil is now flowing out of the tanker and creates a circular iol slick that is about 0.1 foot thick and the radius was calculated to be increasing at .32 foot/minute when the radius of the circle was at 500 feet. NOTE: a typical oil tank is about 330 yards x 60 yards x 30 yards and is close to rectangular box.
A) In general, at what rate is the volume of the ship’s oil decreasing? What is the rate of change of the volume when the spill is at 500 feet? (Volume of oil decreasing = volume of oil increasing)
B) If the oil were to leak at an average rate of that found in part A, how long will it take if the hole in the tank is no repaired before all of the oil has leaked out? (Give answer in number of days.) Note: the hole is in the very bottom of the tank.
C) A little bit of good new. The hole was quite small and it has been plugged. The oil has stopped leaking. Now we must work fast to confine the oil spill when the tank was still half full? Put into perspective how big the oil spill is –how far across the spill is it?
bohemiarapper
Asked Nov 04, 2011
Go to the link below and scroll down to the heading labeled Calculus. There are four videos on Optimization.

http://www.khanacademy.org/
Rob
Answered Nov 05, 2011

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