SOLUTION: A cylindrical tank, with the circular base on the ground, of radius 10 meters, and a height of 20 meters, is filling with water at a rate of 10 cubic meters per second. What is the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A cylindrical tank, with the circular base on the ground, of radius 10 meters, and a height of 20 meters, is filling with water at a rate of 10 cubic meters per second. What is the      Log On


   

Question 1034350: A cylindrical tank, with the circular base on the ground, of radius 10 meters, and a height of 20 meters, is filling with water at a rate of 10 cubic meters per second. What is the rate of change of the height of the water when the height is 10 meters?
Found 2 solutions by ikleyn, Gogonati:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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A cylindrical tank, with the circular base on the ground, of radius 10 meters, and a height of 20 meters,
is filling with water at a rate of 10 cubic meters per second.
What is the rate of change of the height of the water when the height is 10 meters?
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Simply divide the rate of 10 m%5E3 by the area of the cross-section of the cylindrical tank:

dh%2Fdt = 10%2F%28pi%2Ar%5E2%29 = 10%2F%283.14%2A10%5E2%29.

The height of the tank is an excessive data in this problem. 
It is not relevant neither the solution nor the answer.


Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
dv%2Fdt=10%2A+%28m%5E3%2Fs%29 What is dh%2Fdt when h=10m. Since V=pi%2Ar%5E2%2Ahand
dV%2Fdt=pi%2Ar%5E2%2A%28dh%2Fdt%29, since dV%2Fdt=10 we get 10=pi%2A100%2A%28dh%2Fdt%29
and dh%2Fdt=1%2F%2810%2Api%29. The rate of change of the height is 1%2F%2810%2Api%29.