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 nprism?
If n=3 you can't do better than putting your circle on one of the square sides of the prism, so the solution is a circle of diameter 1 and an area of π/4
As n increases the prism approaches a cylinder. In a cylinder you can do no better than the circular base (picture a coin spinning in a tube.) So the limiting area as n increases is that of the circle that can be inscribed in the base. r = 1/(2tan(180/n)) A = πr^2

Posted by Jer
on 20120701 14:27:19 