January 20th, 2010, 01:24 PM  #1 
Newbie Joined: Sep 2009 Posts: 22 Thanks: 0  Polyhedron
Suppose you have an equilateral triangle. The area of the triangle is exactly 1200 square centimetres. Now suppose you have twenty of those triangles. It's possible to assemble those twenty triangles into a closed threedimensional shape, a regular polyhedron. What would be the volume, in cubic centimetres, of the largest sphere that could fit inside the shape? Round to the nearest whole number. Thank you in advance! 
January 20th, 2010, 04:24 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Polyhedron
Sounds like your looking for the volume of a sphere inscribed in an icosahedron.

January 25th, 2010, 02:32 PM  #3 
Newbie Joined: Sep 2009 Posts: 22 Thanks: 0  Re: Polyhedron
ya anytime someone suggests I read something either I don't get it/understand or it's too long and boring...

January 25th, 2010, 02:56 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  Re: Polyhedron
The article gives the formula for the radius of a sphere inscribed in an icosahedron, in terms of the length of the edge of the icosahedron. Since the edge of the icosahedron is the length of the side of the equilateral triangle, you need that length and the formula for the volume, V, of a sphere in terms of radius: . Can you find the length of the side of the triangle? 

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