Question**: A circle has a circumference of 31.4 meters. What is the area of the circle? - MyGigsters
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 circumferenceâa fundamental relationship in geometry. If youâve ever wondered how to calculate the area given just the circleâs 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) â 3.14
- $ r $ = radius of the circle
Since the circumference is 31.4 meters, we can solve for the radius.
Image Gallery
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 $:
$$
r = rac{31.4}{2\pi}
$$
🔗 Related Articles You Might Like:
The Secret of Being THE BEST hits harder than you think You Won’t Believe What It Takes to Prove You’re THE BEST No One Elites Like ME—DEFINITELY YOU ARE THE BESTFinal Thoughts
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.