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Finding the Circumference of a Circle Using Its Shadow

Date: 1/26/96 at 5:23:17
From: Anonymous
Subject: Formula for circumference of circle

I am attempting to find the circumference of a large sphere 
hanging 25 feet in the air.  It occurred to me that I could 
measure the shadow diameter and calculate from there, but I 
have long forgotten the formula and I'm not sure if that's 
the right approach anyway.  I'd sure appreciate some help.

Thank you.
Paul Oldenburg

Date: 1/27/96 at 21:17:13
From: Doctor Ken
Subject: Re: Formula for circumference of circle


Sure, that approach will work fine, as long as I understand 
your question correctly.  You're looking for the length that 
a belt would have to be to go around the big sphere in the air, 

If you measure the diameter of the shadow, then the circumference 
of the circle (and the length of the belt) will be Pi times the 
diameter, and Pi is about 3.14159.

One thing to keep in mind: make sure that the light you're using 
to cast the shadow is pretty far away from the sphere, or else 
the shadow is going to be a lot bigger than the actual sphere 
in the air (consider what happens when the light is REALLY close 
to the sphere - the shadow is really big!).

-Doctor Ken,  The Math Forum
Associated Topics:
High School Conic Sections/Circles
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry

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