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the volume of a rectangular box with a square base remains constant at 500 cm^3 as the area of the box increases at a rate of 3cm^2/sec. find the rate at which the height of the box is decreasing when each side of the base is 18 cm long.

  • calculus -

    500=areabase* h

    take the derivative.

    0=d areabase/dt * h+ areabase*dh/dt

    solve for dh/dt when
    h= 500/18^2
    dareabase/dt=3 cm^2/sec

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