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24 February, 06:10

Water is flowing into a conical tank at a rate of 3 ft3/min. The height of the tank is 10 feet and its diameter is 6 feet. Find the rate at which the height of the water level is changing at the instant its height is 5 feet.

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  1. 24 February, 06:19
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    Dh/dt = 1.273 ft/min

    Step-by-step explanation:

    Volume of cone V = 1/3 * π * r² * h

    Then

    DV/dt = 1/3 * π * r² * Dh/dt (1)

    We have to find out values of r when h = 5

    By symmetry in a cone (we have proportion between h and r

    when h = 10 ft r = 3 ft from problem statement

    Then h = 5 ft r = 1.5 ft

    That is from proportion 3/10 = X/5

    Then by subtitution in (1)

    DV/dt = 3 ft³/min r = 1,5 ft

    3 = 1/3*π * (1.5) ² * Dh/dt

    3 = 2.355 Dh/dt

    Dh/dt = 1.273 ft/min
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