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Circumference and Area of a Circle
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The area of a circle is 36π m². What is the circumference, in meters? Express your answer in terms of piπ.

Answer 1

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

1. The formula for the area \( A \) of a circle is:
\[
A = \pi r^2
\]
where \( r \) is the radius.

2. We know the area is given as \( 36\pi \) m²:
\[
36\pi = \pi r^2
\]

3. Dividing both sides by \( \pi \):
\[
36 = r^2
\]

4. Taking the square root of both sides to find the radius:
\[
r = \sqrt{36} = 6 \text{ m}
\]

5. Now, we can calculate the circumference \( C \) using the formula:
\[
C = 2\pi r
\]

6. Substituting the radius into the circumference formula:
\[
C = 2\pi(6) = 12\pi \text{ m}
\]

Thus, the circumference of the circle is \( \boxed{12\pi} \) meters.