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 circumferenceÃ¢ÂÂa fundamental relationship in geometry. If youÃ¢ÂÂve ever wondered how to calculate the area given just the circleÃ¢ÂÂs 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) Ã¢ÂÂ 3.14
- $ r $ = radius of the circle

Since the circumference is 31.4 meters, we can solve for the radius.

Circumference And Area Of A Circle Worksheet

Image Gallery

Area And Circumference Of A Circle Worksheet - Adriansonfifth

Circumference of a Circle Worksheets - Math Monks - Worksheets Library

How to Find the Circumference and Area of a Circle: 5 Steps

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:

📰 You Won’t Believe What This Runyon Looks Like Under the Sun 📰 Hidden Beauty Inside the Ranunculus – It’s Wilder Than You Think 📰 The Secret Reason Ranunculus Flowers Hold So Much Power 📰 Then V 20000 Times 0614125 Approx 1228250 📰 Then W 50 25 25 The Maximum Area Is 📰 Then X20 X 96 📰 Then 13 Of 16 16 13 163 5333 Still Not Integer But 48 Divisible By 3 Yes 48 3 16 13 Of 16 Is Not Integer But 16 Not Divisible By 3 Problem But In Math Problems Accept Fractional Intermediate 📰 Then The Length Is 3W 📰 Therefore No Angle That Is A Non Multiple Of 90 Can Be Reached If Its A Multiple Of 45 Because 45 And 18 Generate The Subgroup Of 9Z But The Intersection With Multiples Of 45 Is Multiples Of 90 📰 Therefore The Maximum Value Is Boxed2 📰 Therefore The Total Time Required Is 8 Hours 📰 These 1 Books For 4Th Graders Are Taking Social Media By Stormyour Kid Will Too 📰 These 10 Black Romance Movies Will Steal Your Heart Overnight 📰 These 10 Blue Logos Are Going Viral Are You Ready To Copy Them 📰 These 10 Bob Dylan Album Covers Will Blow Your Mind Hidden Meanings Revealed 📰 These 10 Booz Allen Hamilton Photos Will Change How You See Top Tech Spies 📰 These 10 Full Flavored Boba Balls Are Taking Over Cafsready To Join The Swirl 📰 These 3 Hidden Bones In Your Foot Will Change How You Walk Forever

Final 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.