SOLUTION: A cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet. The oil begins draining at a constant rate of 2 cubic feet per second. [Hint: depth and volu
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Question 678353: A cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet. The oil begins draining at a constant rate of 2 cubic feet per second. [Hint: depth and volume are not the same]
a) Write the volume of the oil remaining the tank t seconds later as a function of t.
b) Write the depth of the oil remaining in the tank t seconds later as a function of t.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A cylindrical tank with a diameter of 20 feet is filled with oil to a depth of 40 feet.
:
Find the original volume of the oil; (radius = 10 ft)
V =
V = 12566.37 cu/ft of oil
:
The oil begins draining at a constant rate of 2 cubic feet per second. [Hint: depth and volume are not the same]
a) Write the volume of the oil remaining the tank t seconds later as a function of t.
V = 12566.37 - 2t
:
b) Write the depth of the oil remaining in the tank t seconds later as a function of t.
Find the depth (x) of 2 cu ft in this tank, let
= 2
x =
x = .0063662 ft per second at a 2 cu/ft per second rate
d = 40 - .0063662t
:
:
We can check this by finding how long it will take to empty the tank
12566.37/2 = 6283.2 seconds
Find the depth of oil drained in this time
6283.2 * .0063662 = 40.00 ft
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