Sunday, 30 November 2014

calculus - What is the maximum volume of an equilateral triangular prism inscribed in a sphere of radius 2?

What is the maximum volume of an equilateral triangular prism inscribed in a sphere of radius 2?

Since the volume of an equilateral triangular prism is $\frac{\sqrt3}{4}a^2h$,where $a$ is the side length of the base triangle and $h$ is the height of the prism.How to express this volume in terms of radius of the sphere so that i can differentiate it and equate it to zero.Thanks.

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