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Circle in a Prism (Posted on 2012-06-30) Difficulty: 4 of 5
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?


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

No Solution Yet Submitted by K Sengupta    
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n=4 (the easy one) | Comment 1 of 2
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
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