Question**: A circle has a circumference of 31.4 meters. What is the area of the circle? - Decision Point
Question: A circle has a circumference of 31.4 meters. What is the area of the circle?
Question: A circle has a circumference of 31.4 meters. What is the area of the circle?
Understanding the area of a circle starts with knowing its circumferenceâÃÂÃÂa fundamental relationship in geometry. If youâÃÂÃÂve ever wondered how to calculate the area given just the circleâÃÂÃÂs circumference, this article will guide you step-by-step through the process using a real-world example: a circle with a circumference of 31.4 meters.
What Is Circumference and Why Does It Matter?
Understanding the Context
Circumference is the total distance around the edge of a circle, measured in meters (or any unit of length). The formula to calculate circumference is:
$$
C = 2\pi r
$$
where:
- $ C $ = circumference
- $ \pi $ (pi) âÃÂà3.14
- $ r $ = radius of the circle
Since the circumference is 31.4 meters, we can solve for the radius.
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Key Insights
Step 1: Solve for the Radius
Using the circumference formula:
$$
31.4 = 2\pi r
$$
To isolate $ r $, divide both sides by $ 2\pi $:
$$
r = rac{31.4}{2\pi}
$$
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Substituting $ \pi pprox 3.14 $:
$$
r = rac{31.4}{2 \ imes 3.14} = rac{31.4}{6.28} = 5 \ ext{ meters}
$$
So, the radius of the circle is 5 meters.
Step 2: Use the Radius to Calculate the Area
The area $ A $ of a circle is calculated with the formula:
$$
A = \pi r^2
$$
Now plug in $ r = 5 $:
$$
A = \pi \ imes 5^2 = \pi \ imes 25 pprox 3.14 \ imes 25 = 78.5 \ ext{ square meters}
$$
Final Answer
A circle with a circumference of 31.4 meters has an area of 78.5 square meters.
