calculus

1. A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

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  1. dv = pi r^2 dh
    where
    r = (12/24)h = .5 h
    so
    dv = pi (.25)h^2 dh
    dv/dt = .25 pi h^2 dh/dt
    when h = 5
    dv/dt = (25 pi/4 )dh/dt
    dv/dt = (25 pi/4)(4)

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