42e359…: “Behind a windy ocean”

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A right circular cone is to be made with a fixed slant height of 8 ft.

The height that maximizes the volume of the cone is

\[ h = \answer {\frac {8}{\sqrt {3}}} \]

Hint: The volume of the cone is $\frac {\pi r^2h}{3}$, where $h$ is the height of the cone and $r$ is the radius.