In a time long long ago in a land far far away (okay, maybe not that far)...

As a reward for your clever calculating services, the High King Math offers you a reward. This kingdom molds its gold into right circular cone shapes for currency, and the King will grant mold you such a cone that follows the following criteria:

You may choose the radius ® and height (h) of the cone, but it must fit, placed upside down, in a larger cone of radius R and height H, with the bases of the two cones parallel (sketched below).

In terms of R and H, what values should you choose for your cone to get the most gold?

Place one right circular cone upside down inside a larger one so that their bases are parallel as sketched below. Find the values of r and h that maximize the area of the smaller cone.

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## Yoruichi-san

In a time long long ago in a land far far away (okay, maybe not that far)...

As a reward for your clever calculating services, the High King Math offers you a reward. This kingdom molds its gold into right circular cone shapes for currency, and the King will grant mold you such a cone that follows the following criteria:

You may choose the radius ® and height (h) of the cone, but it must fit, placed upside down, in a larger cone of radius R and height H, with the bases of the two cones parallel (sketched below).

In terms of R and H, what values should you choose for your cone to get the most gold?

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