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