The circumference of a circle is 20π m. What is the area, in square meters? Express your answer in terms of π

To find the area of the circle given its circumference, we can use the following steps:

1. Understanding the formula for circumference: The circumference (C) of a circle is given by the formula:

[

C = 2pi r

]

where (r) is the radius.

2. Setting up the equation: According to the problem, the circumference is (20pi) m. We can set the equation:

[

2pi r = 20pi

]

3. Solving for the radius: We can simplify this equation. Dividing both sides by (2pi):

[

r = frac{20pi}{2pi} = 10 text{ m}

]

4. Using the radius to find the area: The area (A) of a circle is given by the formula:

[

A = pi r^2

]

Substituting the radius we found:

[

A = pi (10)^2 = pi times 100 = 100pi

]

Therefore, the area of the circle is (100pi) square meters. Keep up the great work! If you have more questions, feel free to ask!