My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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 three-dimensional 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!
mydisguise08 is offline  
 
January 20th, 2010, 04:24 PM   #2
Global Moderator
 
greg1313's Avatar
 
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.
greg1313 is offline  
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...
mydisguise08 is offline  
January 25th, 2010, 02:56 PM   #4
Global Moderator
 
greg1313's Avatar
 
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?
greg1313 is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
polyhedron



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
convex polyhedron alex2010 Algebra 0 June 13th, 2012 03:10 AM
Polyhedron puzzle sivela Algebra 1 April 26th, 2009 03:29 PM
polyhedron milko Algebra 1 August 5th, 2008 07:30 AM





Copyright © 2019 My Math Forum. All rights reserved.