How do I find the area of a circle using circumference?

Question

asked Dec 12, 2023 185k views

1 Answer

AlwaysStudent · Answer 1 · 2023-12-18T07:12:44+0000

We know that the circumference has the following formula:

$\text{C = 2}\cdot\pi\cdot r$

and that the formula for the area of a circle is:

$A\text{ = }\pi\cdot r^2$

Therefore, by means of the circle formula we solve the radius, like this:

$\text{r = }(C)/(2\pi)$

Now, we simply replace in the area formula, as follows:

$\text{A = }\pi\cdot((C)/(2\pi))^2$

In this way, you would have the area of the circle as a function of the circumference.