Associated Topics || Dr. Math Home || Search Dr. Math

### 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.

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/
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search