Maximizing the Volume of a Right Circular Cone with Given Slant Length

Given the slant length of a right circular cone, find the value of the angle between the axis and a generator of the cone that maximizes the volume of the cone with that slant length.


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This is a typical maximization problem encountered by calculus students as an application of differentiation.
[1] F. Curmi, J. Spiteri, and C. Vassallo, Pure Mathematics 1B, Malta: Progress Press, 2006 p. 100, example 2.20.
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