# Volume of a circle

1. Jun 18, 2009

### Ry122

http://users.on.net/~rohanlal/circle2.jpg [Broken]
this is part of the solution to finding the volume of a circle with double integrals.
I just want to know where the r from rdrd0 came from and also
why the limits on the d0 integral are 2pi and 0.

Last edited by a moderator: May 4, 2017
2. Jun 18, 2009

### Hootenanny

Staff Emeritus
I assume you mean this is part of a question to find the volume of the cylinder created by extruding a circle along the z-axis.

To answer your first question, the integral has be transformed from Cartesian to polar coordinates. Rather than specifying the position of a point in terms of it's (x,y) coordinates, polar coordinates uses (r,Θ), where r is the distance from the origin to the point and Θ is the angle between the radius and the positive x semi-axis. For more information and answers to your subsequent questions see http://mathworld.wolfram.com/PolarCoordinates.html" [Broken].

Last edited by a moderator: May 4, 2017
3. Jun 18, 2009

### Ry122

What makes you think its a cylinder?
This is the full solution:
http://users.on.net/~rohanlal/circ3.jpg [Broken]

Last edited by a moderator: May 4, 2017
4. Jun 18, 2009

### HallsofIvy

Staff Emeritus
This is the volume of a sphere, not a circle- circles don't have "volume"!

And you should have learned that the "differential of area in polar coordinates" is $r dr d\theta$ when you learned about integrating in polar coordinates. There are a number of different ways of showing that. I recommend you check your calculus book for the one you were expected to learn.

Last edited by a moderator: May 4, 2017
5. Jun 18, 2009

### Ry122

and why is the limit 2pi to 0?

6. Jun 19, 2009

### Hootenanny

Staff Emeritus