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=(C)/(2\pi)=(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=(25)/(4)\pi_{\text{ }}in^2 \end{gathered}`