What is the formula for the area of a circle?

2 Answers
Mar 3, 2017

#A=pi*r^2=# area of a circle

Mar 3, 2017

Answer:

The formula #A = pi r^2# expresses the area of a circle in terms of its radius.

Explanation:

The number #pi# is defined as the ratio of the circumference of a circle to its diameter (i.e. to twice its radius), hence the formula #2 pi r#.

The area of a circle is given by the formula:

#A = pi r^2#

To see why, you can divide a circle into a number of equal segments and stack them head to tail to form a sort of parallelogram with 'bumpy' sides. The long sides will be about half the circumference in length - that is #pi r#, while the height of the parallelogram will be about #r#. So the area is seen to be about #pi r^2#.

This approximation gets better the more segments you have, but here's an animated illustration I put together with just #8# segments...

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