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Mathematics-Online problems:

Interactive Problem 177: Extremal Ratio of Volume to Lateral Area of a Circular Cone

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A piece of paper in the shape of a sector of a circle with radius $ r$ and a central angle of the sector $ \varphi\in(0,2\pi)$ is glued together along the dotted lines without overlapping, thus obtaining a circular cone.

\includegraphics[width=.3\linewidth]{g61_bild1.eps}          $ \longrightarrow$          \includegraphics[width=.24\linewidth]{g61_bild2.eps}

For which angle $ \varphi$ does the ratio of the volume of the cone to its lateral surface area become a maximum?

Answer:

$ \varphi$ =

(The result should be correct to four decimal places.)


   

(Authors: Wipper/Walter)
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  automatically generated: 8/11/2017