Question

The circumference of a circle is 5π in. What is the area, in square inches? Express your answer in terms of \piπ.

Answer 1

The circumference is given by:

$\begin{gathered} C=2\pi r \\ Since: \\ C=5\pi \\ Solve_{\text{ }}for_{\text{ }}r: \\ r=\frac{C}{2\pi}=\frac{5\pi}{2\pi}=2.5 \end{gathered}$

Now we know the radius of the circle we can find the area as follows:

$\begin{gathered} A=\pi r^2 \\ A=(2.5^2)\pi \\ Answer: \\ A=6.25\pi_{\text{ }}in^2 \\ or_{\text{ }}as_{\text{ }}a__{\text{ }}fraction: \\ A=\frac{25}{4}\pi_{\text{ }}in^2 \end{gathered}$