Homework:

$4\mathrm{.}5$ HW $-$

Optimization

Question

Completed: $10$ of $12$

My score: $9\mathrm{.}5/12$ pts $(79\mathrm{.}17\%)$

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Problems

A right circular cone is inscribed inside a larger right circular cone with a volume of $120c{m}^3.$ The axes of the cones coincide, and the vertex of the inner cone touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner cone.

The ratio of the height of the inner cone to the height of the outer cone is $$