The area of a circle in terms of the circumference

HOME

Math Central

Quandaries & Queries

Question from Sarah, a student:

How do you find the area of a circle if you already have the circumference?
There was one answer to this question already but it didn't make sense to
me, because they rounded up pi which you can't do so the answer is
incorrect. thanks

Hi Sarah,

We often see the circumference $C$ of a circle of radius $r$ given as

\[C = 2 \pi \; r\]

and the area $A$ as

\[A = \pi \; r^2 .\]

Solve the first equation for $r,$ substitute into the second equation and solve for $A$ to see $A$ as a function of $C.$

Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.