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Math Help - Confusing related rates problem

  1. #1
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    Confusing related rates problem

    This problem has me extremely confused, would really appreciate some help..

    A right circular cone and a hemisphere have the same base, and the cone is inscribed in the hemisphere. The figure is expanding in such a way that the combined surface area of the hemisphere and its base is increasing at a constant rate of 18 square inches per second. At what rate is the volume of the cone changing at the instan when the radius of the common base is 4 inches?

    As i said, im extremely confused and have nothing....Thanks in anyone can help!!
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  2. #2
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    Quote Originally Posted by alakaboom1 View Post
    This problem has me extremely confused, would really appreciate some help..

    A right circular cone and a hemisphere have the same base, and the cone is inscribed in the hemisphere. The figure is expanding in such a way that the combined surface area of the hemisphere and its base is increasing at a constant rate of 18 square inches per second. At what rate is the volume of the cone changing at the instan when the radius of the common base is 4 inches?

    As i said, im extremely confused and have nothing....Thanks in anyone can help!!
    surface area of hemisphere and base ...

    A = 2\pi r^2 + \pi r^2 = 3\pi r^2

    \frac{dA}{dt} = 6\pi r \frac{dr}{dt}

    you are given values for r and \frac{dA}{dt}, find \frac{dr}{dt}


    volume of the cone (note height of cone is r of hemisphere) ...

    V = \frac{\pi}{3} r^3

    \frac{dV}{dt} = \pi r^2 \frac{dr}{dt}

    evaluate \frac{dV}{dt}
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  3. #3
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    ahhh.....i see. i failed to realize that h was equal to r. Thank you so much.
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