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Question
A conical tank (with vertex down) is 20 ft across the top and 24 ft deep. Water is flowing in to the tank at a rate of 15 ft^3/min when the height of the water is 10 ft. Find the rate of the change of the height of the water.
The volume of a conical tank is pi*r^2*h/3 where r is the radius and h is the height. We know that the radius is 10/24 of 20. The rate of change of volume is a constant 15.
What needs to be done is to find the formula for volume in terms of height (that's where the 20/24 is used), so take the derivative of of volume in terms of height, and then put in the factors.
What you'll get is a dV/dt equal to something times dh/dt. dV/dt is equal to 15, so solve for dh/dt.
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Scotto
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