Question

The circumference of a circle is 13π in. What is the area, in square inches? Express your answer in terms of pie.

Answer 1

The circumference (C) of a circle with radius r is:

`C=2\pi r`

Given the measure of the circumference (13π in), first, let's substitute it in the equation find r:

`\begin{gathered} 13\pi=2\pi r \\ \text{ Dividing both sides by 2}\pi\text{:} \\ (13\pi)/(2\pi)=(2\pi)/(2\pi)r \\ (13)/(2)=r \\ r=(13)/(2)\text{ in} \end{gathered}`

The area (A) of a circumference with radius r is:

`A=\pi r^2`

Knowing r, substitute it to find A:

`\begin{gathered} A=\pi r^2 \\ A=\pi *((13)/(2))^2 \\ A=42.25\text{ in}^2 \end{gathered}`

Answer: Area = 42.25 in².