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Math Help - Maximum volume

  1. #1
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    Maximum volume

    A sector with central angle (theta) is cut from a circle of radius 12 inches and the edges of the sector are brought together to form a cone. Find the magnitude of theta such that the volume of the cone is a maximum.
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  2. #2
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    Re: Maximum volume

    Quote Originally Posted by jellchavez View Post
    A sector with central angle (theta) is cut from a circle of radius 12 inches and the edges of the sector are brought together to form a cone. Find the magnitude of theta such that the volume of the cone is a maximum.
    s=12

    2r\pi=\frac{s\pi\theta}{180}

    hence

    r=\frac{s\theta}{360}

    V=\frac{r^2 \pi H}{3} and H=\sqrt{s^2-r^2}

    Now , find \theta from V'_{\theta}=0
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