The Murderous Maths Research Lab proudly presents...

THE AREA OF AN ANULUS
####
An anulus is like a disc with a round hole in it and you can get the area with just
one measurement.

All you do is draw a straight line across the ring that just touches the little circle in the
middle. If the length of this line is L then:

The area of the anulus is pi x (L/2)^{2}

But why?

The answer is rather satisfying. Obviously the area is the same as the little circle taken away from the
big circle, so let's see what happens when we try it. Remember the
area of a circle = PI x r^{2} where
r is the radius of the circle (a radius is the distance from the middle to the edge).

Here we've called the radius of the big circle R and the little one is r.

- The area of the big circle is PI x R
^{2}
- The area of the little circle is PI x r
^{2}
- So the area of the anulus is PI x R
^{2} - PI x r ^{2} =
PI x (R^{2} - r^{2})

But now look at the diagram - we've got a right angled triangle. If you've read
Vicious Circles you'll know all about PYTHAGORAS, and you'll see that
R^{2} = (L/2)^{2} + r^{2}. Therefore
- R
^{2} - r^{2} = (L/2)^{2}
- Swap this into our answer above and we get
area of anulus= PI x (L/2)
^{2}

*We'd like to thank Alex Jeffreys for bringing this neat formula to our attention!*

To the Research Lab

To the Area Calculator Page

Murderous Maths Main Index Page