Ellipses and Ellipsoids
The Area of an Ellipse
You'll find lots of formulas for getting the areas of different shapes
in Desperate Measures
but ellipses are just that little bit harder to work out!
The formulas for ellipses and ellipsoids plus over 170 other things are all in The Perfect Sausage
Here's our way:
- Put the ellipse inside the smallest rectangle you can
- Work out the area of the rectangle ( by multipling the lengths of the
- Divide the area of the rectangle by 4
- Finally multiply by pi!
If putting the ellipse into a rectangle looks too tough, you can just measure
how long it is to get A, and then measure how fat it is to get B, then multiply the
two results together. You then divide by 4 and multiply by pi.
- The length A is often called the "Major Axis" and B is the "Minor Axis".
Sometimes you're given the lengths of the "longest radius" (shown here as a)
and the "shortest radius" (shown here as b). Obviously in our diagrams
a = ½A and b = ½B in which case you get this formula:
Of course the EASIEST way to work out the area of an ellipse is to use our
Thanks to JAKE CHAN who was the first person to
contact us and ask about ellipses!
The Volume of an Ellipsoid
In the same way that a circle turns into a solid sphere, an ellipse can become
a solid "ellipsoid".
There are two special types of ellipsoid.
Suppose you get a sphere and stretch it to make a longer and thinner shape
(a bit like a rugby ball or a melon) this is called a PROLATE ELLIPSOID.
If you chop it in half to get a circle, then the volume is the area of the circle
times by 2/3rds of the major axis. (The major axis is the maximum length from one end to another.)
However if you get a sphere and squash it to make a shorter fatter shape
(a bit like a SMARTIE or a burger) this is called an OBLATE ELLIPSOID.
If you chopped it through the middle to get a circle, then the volume is
the area of the circle times by 2/3rds of the minor axis. (If your "burger" is lying flat on a table, the minor axis is the height.)
Many thanks to "Pete" who contacted us with corrections to this page in April 2005.
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