Dividing a Cylinder

Date: 08/06/2001 at 08:56:22
From: Jon
Subject: Cylinders

I have a cylinder that is 4 by 9 inches. Can it be divided into two 
separate parts and still have the same volume? Like two smaller 
cylinders. I have used the formulas but I can not seem to get it. 
Could you please help? Thank you.

Jon

Date: 08/06/2001 at 22:11:53
From: Doctor Jaffee
Subject: Re: Cylinders

Hi Jon,

I'm assuming that you have a cylinder whose base has a diameter of 
4 inches and the height of the cyinder is 9 inches. Since volume is 
pi*(r^2)*h, the volume of this cylinder is pi*(2^2)*9 = 36pi cubic 
inches.

If the cylinder were made out of paper, you could slice it along its 
height and make a rectangle whose length is 9 inches and whose width 
would be the circumference of the base of the cylinder, 4pi inches.

Cut this rectangle into 4 strips, each measuring 4pi x 9/4 inches.

Take two of the strips and put them together to make a rectangle with 
dimensions 8pi x 9/4 inches.  This rectangle can be rolled up to make 
a cylinder whose base has a diameter of 8 inches and whose height is 
9/4 inches. The volume of this cylinder is 36pi cubic inches.

I hope my answer has helped you understand the problem better.  If you 
want to discuss it more, or if you have other questions, write back.  
Thanks for writing to Ask Dr. Math.

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