An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. if water is flowing in at a rate of 12 f
t3/min, find the rate of change of the depth of the water when the water is 10 feet deep.
1 answer:
Let
dV = dt = water is flowing in at a rate of 12 ft3 / min.
h = the depth of the water.
dh / dt = the rate of change of the depth.
First you must find the volume of the cone as a function of "h". Then you must derive the volume of the cone with respect to time. Finally clear dh / dt.
I attach the solution.
dV = dt = water is flowing in at a rate of 12 ft3 / min.
h = the depth of the water.
dh / dt = the rate of change of the depth.
First you must find the volume of the cone as a function of "h". Then you must derive the volume of the cone with respect to time. Finally clear dh / dt.
I attach the solution.
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