SOLUTION: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 20 cubic feet per minute. Find the rate of change of the d

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Question 1130066: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 20 cubic feet per minute. Find the rate of change of the depth of the water when the water is 4 feet deep.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
10 feet across the top => d=10ft => r=5ft
and 12+feet deep=> h=12ft
Water is flowing into the tank at a rate of dV%2Fdt=20+ft%5E3%2Fmin
the water is 4 feet deep=> h%5B1%5D=4ft
find: dh%2Fdt
r%2Fh=5%2F12
12r=5h
r=5h%2F12

V=%281%2F3%29pi%2Ar%5E2%2Ah

V=%281%2F3%29pi%2A%285h%2F12%29%5E2%2Ah

V=%281%2F3%29pi%2A%2825h%5E2%2F144%29%2Ah

V=%281%2F3%29pi%2A%2825%2F144%29h%5E3


dV%2Fdt=%281%2F3%29pi%2A%2825%2F144%29%2A3h%5E2%28dh%2Fdt%29

dV%2Fdt=%281%2Fcross%283%29%29pi%2A%2825%2F144%29%2Across%283%29h%5E2%28dh%2Fdt%29

dV%2Fdt=pi%2A%2825%2F144%29%2Ah%5E2%28dh%2Fdt%29

dV%2Fdt=%2825%2Ah%5E2%2Api%29%2F144%28dh%2Fdt%29..........multiply by recip.

%28dh%2Fdt%29=144%2F%2825%2Ah%5E2%2Api%29%28dV%2Fdt%29..........since h=4, and dV%2Fdt=20+ we have

%28dh%2Fdt%29=144%2F%2825%2A4%5E2%2Api%29%2820%29



%28dh%2Fdt%29=9%2F%285%2Api%29%284%29

%28dh%2Fdt%29=36%2F%285%2Api%29+%28ft%2Fmin%29