Triangle Proportions: A Diagram

Date: 05/06/2003 at 22:11:32
From: Brandon
Subject: Finding the length of a side of a cube inside a cone

A cone has a circular base radius 1, and vertex of height 3 directly 
above the center of the circle. A cube has four vertices in the base 
and four on the sloping sides. What is the length of a side of the 
cube?  Answer to 5 decimal places.

Acircle = pi r squared
Acircle = 3.1416
v = 1/3 AB H 
v = 1/3 x 3.1416 x 3
Vcone = 3.1416

Date: 05/07/2003 at 08:54:18
From: Doctor Luis
Subject: Re: Finding the length of a side of a cube inside a cone

Hi Brandon,

You don't need to find the volume or area of anything in this problem. 
Rather, you just use the theory of proportions.

Since a picture is worth a thousand words, here's a diagram:



I hope this helped! Let us know if you have any more questions.

- Doctor Luis, The Math Forum
  http://mathforum.org/dr.math/