Question

Circumference and Area of a Circle
Question
The circumference of a circle is 17π m. What is the area, in square meters? Express your answer in terms of piπ.

Answer 1

To find the area of a circle given its circumference, we can use the formulas for circumference and area:

1. The formula for the circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
where \( r \) is the radius of the circle.

2. The area \( A \) of a circle is given by:
\[
A = \pi r^2
\]

Given the circumference is \( C = 17\pi \) m, we can set this equal to the formula for circumference to find the radius \( r \):
\[
2\pi r = 17\pi
\]

Dividing both sides by \( 2\pi \):
\[
r = \frac{17\pi}{2\pi} = \frac{17}{2} \text{ m}
\]

Now, we can calculate the area using the radius we found:
\[
A = \pi r^2 = \pi \left( \frac{17}{2} \right)^2
\]

Calculating \( \left( \frac{17}{2} \right)^2 \):
\[
\left( \frac{17}{2} \right)^2 = \frac{17^2}{2^2} = \frac{289}{4}
\]

Now substituting this back into the area formula:
\[
A = \pi \cdot \frac{289}{4} = \frac{289\pi}{4} \text{ square meters}
\]

Thus, the area of the circle is:
\[
\boxed{\frac{289\pi}{4}} \text{ square meters}
\]