Given a regular right hexagonal prism of edge length 1, what is the largest circle (in terms of area) that can be placed completely inside the prism?

Extension:

What is the largest circle (in terms of n) that can be placed completely inside a regular right unit n-prism?

In a cube it's pretty easy.  Join one midpoint of each side to make the regular hexagonal cross section.  The sides of this hexagon are √2/2 and so the radius of the inscribed circle is √6/4.  The area of this circle is thus 3π/8.

Posted by Jer on 2012-07-01 00:29:51