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A conical tank (with its vertex down) is 8 feet tall and 6 feet across its diameter. If water is flowing into the tank at the rate of 2 feet3/min, find the rate at which the water level is rising at the instant when the water depth is 2.5 feet.

  • Math -

    Water depth = y
    Surface water radius r = 3 y/8 ft

    Water volume V = (1/3)*pi*(3y/8)^2*y
    = (3 pi/64)y^3

    dV/dt = 2.0 ft^3/min = (9*pi*y^2/64)*dy/dt = pi*r^2*(dy/dt)

    When y = 2.5 ft
    dy/dt = 4.53 ft/min

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