# Calculus 1

A filter filled with liquid is in the shape of a vertex-down cone with a height of 12 inches and a diameter of 18 inches at its open (upper) end. If the liquid drips out the bottom of the filter at the constant rate of 5 cubic inches per second, how fast is the level of the liquid dropping when the liquid is 2 inches deep?

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1. at a time of t seconds ...
let the radius of the circular water level be r
let the height of the water be h

12/9 = h/r
12r = 9h
4r = 3h ----> r = 3h/4

V = (1/3)π r^2 h
= (1/3)π (9h^2/4)(h)
= (3/4)π h^3

dV/dt = (9/4) h^2 dh/dt
5 = (9/4)π (4) dh/dt
solve for dh/dt

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posted by Reiny

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