Question

the circumference of a circle is 17π m. what is the area, in square meters? express your answer in terms of π.

Explanation:

Step1: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=17\pi\), we have \(17\pi=2\pi r\). Dividing both sides by \(2\pi\), we get \(r=\frac{17}{2}\) m.

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = \frac{17}{2}\) into the formula: \(A=\pi(\frac{17}{2})^{2}=\pi\times\frac{289}{4}=\frac{289\pi}{4}\) \(m^{2}\).

Answer:

\(\frac{289\pi}{4}\) square meters