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Math Help - Optimization Problem about a cone

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    Optimization Problem about a cone

    Find the greatest possible volume for a circular cone having a given slant height??? I don't know how to attempt this
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    Quote Originally Posted by Mathforum View Post
    Find the greatest possible volume for a circular cone having a given slant height??? I don't know how to attempt this
    let s = fixed slant height

    r^2 + h^2 = s^2

    V = \frac{\pi}{3}r^2 h

    V = \frac{\pi}{3}(s^2-h^2) h

    V = \frac{\pi}{3}(s^2h-h^3)


    find \frac{dV}{dh} and maximize ... remember that s is a constant.
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    Thank you so much that helped a lot!!
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