A water tank has the shape of an upright cylinder. The cylinder is filling at a rate of 1.5 m^3 / minute. If the tank has a radius of 2 m, at what rate is the water level increasing when the water is 3.2 m deep?

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Answer 1 · 2016-07-19T11:39:11

#1.5 /(4 pi) m/min approx 0.12m/min#

Cylinder volume #V = pi r^2 h#

differentiate wrt time

#dot V = pi r^2 dot h#
#implies dot h = dot V /(pi r^2)#

so with upright cylinder the water level increases at a rate that is independent of level itself so that piece of info is redundant

thus:
# dot h = 1.5 /(pi 2^2) approx 0.12m/min#