My Math Forum  

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

Geometry Geometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 1st, 2017, 11:00 PM   #1
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 187
Thanks: 23

Math Focus: Number theory
Volume/(Surface area * edge * number of corners)

Does this quantity differ only +/- 10% for Platonic solids? How about for other groups of solids?
Loren is offline  
 
February 2nd, 2017, 01:04 PM   #2
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 187
Thanks: 23

Math Focus: Number theory
For a tetrahedron, volume=(2^.5/12)a^3, surface area=(3^.5)a^2, edge=a, corners=4

For a cube, volume =a^3, surface area=6a^2, edge=a, corners=8

For an octahedron, volume=(2^.5/3)a^3, surface area=2(3^.5)a^2, edge=a, corners=6

For a dodecahedron, volume=(7.663...)a^3, surface area=(20.646...)a^2, edge=a, corners=20

For an icosahedron, volume=(2.182...)a^3, surface area=(8.660...)a^2, edge=a, corners=12

volume/(surface area * edge * number of corners)=?

Last edited by Loren; February 2nd, 2017 at 01:11 PM.
Loren is offline  
February 4th, 2017, 05:08 PM   #3
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 187
Thanks: 23

Math Focus: Number theory
volume/(surface area * edge * number of corners)=P

For a tetrahedron_____.01701...=P

For a cube_____.02083...=P

For an octahedron_____.02268...=P

For a dodecahedron_____.01856...=P

For an icosahedron_____.02100...=P

Can you explain this cluster of values given P for Platonic solid geometries?
Loren is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
area, corners, edge, number, volume or surface



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Volume,area of surface? ricsi046 Real Analysis 3 April 28th, 2014 01:47 PM
Surface area and volume winner Calculus 3 January 14th, 2011 12:30 PM
surface area to volume? captainglyde Algebra 2 February 19th, 2008 09:30 AM
Surface area and volume winner Algebra 2 January 1st, 1970 12:00 AM
sphere volume surface area kapital Elementary Math 0 January 1st, 1970 12:00 AM





Copyright © 2017 My Math Forum. All rights reserved.