Area of a circle given its circumference

Text

A circle has length $18\pi$ cm. Find the radius and the area of the corresponding disk.

Solution

From the length $C=2\pi r$: $18\pi=2\pi r\ \Longrightarrow\ r=9\ \text{cm}.$ Area of the disk: $\mathcal A=\pi r^2=81\pi\approx254.47\ \text{cm}^2.$ $\boxed{r=9\ \text{cm};\ \ \mathcal A=81\pi\approx254.47\ \text{cm}^2}$