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103 LearnersLast updated on October 7, 2025
Perimeter of Circles
The perimeter of a shape is the total length of its boundary. The perimeter of a circle is known as its circumference. It is used in various practical applications such as designing circular tracks, calculating the length of material needed for circular objects, and more. In this topic, we will learn about the perimeter of a circle.
What is the Perimeter of a Circle?
The perimeter of a circle is called its circumference. It is the total distance around the circle.
The formula for the circumference of a circle is 𝐶 = 2πr, where r is the radius of the circle.
For instance, if a circle has a radius of r = 5, then its circumference is C = 2π(5) = 10π.
Formula for Perimeter of Circle - 𝐶 = 2πr.
Let’s consider another example of a circle with a radius of r = 7. So the circumference of the circle will be: 𝐶 = 2πr = 2π(7) = 14π.
How to Calculate the Perimeter of Circle
To find the perimeter of a circle, we just need to apply the given formula and multiply the radius by 2π. For instance, if a given circle has a radius of r = 4. Perimeter = 2πr = 2π(4) = 8π.
Example Problem on Perimeter of Circle -
For finding the circumference of a circle, we use the formula, 𝐶 = 2πr.
For example, let’s say, r = 3 cm.
Now, the circumference = 2π(3) = 6π cm.
Therefore, the circumference of the circle is 6π cm.
Tips and Tricks for Perimeter of Circle
Learning some tips and tricks makes it easier for children to calculate the circumference of circles. Here are some tips and tricks given below:
- Always remember that a circle's circumference is simply the diameter times π, or 2π times the radius. For that, use the formula, 𝐶 = 2πr.
- Calculating the circumference of a circle starts by determining the radius or diameter. The radius is half the diameter.
- To reduce confusion, make sure to identify whether you are given the radius or diameter before applying the formula.
- To avoid mistakes when calculating the circumference, ensure the radius or diameter is measured accurately and consistently for applications like crafts and construction.
- If you are given the diameter, simply divide it by 2 to find the radius, and then use the formula for the circumference.
Common Mistakes and How to Avoid Them in Perimeter of Circle
Did you know that while working with the perimeter of a circle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Confusing radius with diameter when applying the formula.
Remember that the radius is half the diameter. Always ensure you are using the correct value in the formula 𝐶 = 2πr.
Mistake 2
Students may confuse the concepts of area and circumference, leading to incorrect calculations.
It is important to note that the circumference, calculated in linear units, is the total length around the circle, while the area, in square units, represents the space inside the circle.
Mistake 3
Using approximate values of π without rounding correctly, which can lead to errors in precision.
For higher precision, use more decimal places for π. Common approximations include 3.14 or 22/7.
Mistake 4
Forgetting to multiply by 2 when using the radius for the circumference formula.
Ensure to use the full formula, 𝐶 = 2πr, to account for the entire perimeter of the circle.
Mistake 5
Misreading a problem or mislabeling the radius or diameter.
Double-check the problem and ensure that you're using the correct measurements for your circle.
Perimeter of Circle Examples
Problem 1
A circular garden has a circumference of 62.8 meters. If the diameter of the garden is 20 meters, verify the circumference.
The circumference is correct.
Explanation
Given diameter = 20 meters. Radius r = diameter/2 = 10 meters. Using formula: C = 2πr = 2π(10) = 20π ≈ 62.8 meters. Therefore, the given circumference is correct.
Problem 2
A circular track has a diameter of 50 meters. Find the length of the perimeter of the track.
The perimeter is 50π meters.
Explanation
Given diameter = 50 meters. Radius r = diameter/2 = 25 meters. Using formula: C = 2πr = 2π(25) = 50π meters. Therefore, the length of the perimeter of the track is 50π meters.
Problem 3
Find the circumference of a circle with a radius of 8 cm.
16π cm
Explanation
Circumference of circle = 2πr C = 2π(8) = 16π Therefore, the circumference of the circle is 16π cm.
Problem 4
Sarah is planning to put a fence around her circular swimming pool. The pool has a radius of 6 meters. How much fencing material should Sarah buy?
Sarah will need 12π meters of fencing material.
Explanation
The circumference of the pool is the amount of fencing material needed. Using the formula: C = 2πr C = 2π(6) = 12π meters.
Problem 5
Find the perimeter of a circular walking path with a radius of 15 meters.
Perimeter = 2π(15) = 30π meters.
Explanation
The perimeter of the circular path is calculated using the formula for circumference. By multiplying the radius by 2π, the entire distance around the path is 30π meters.
FAQs on Perimeter of Circles
1.Evaluate the circle’s circumference if its radius is 3 cm.
2.What is meant by a circle’s perimeter?
3.What are the types of circles?
4.What value is used for π in calculations?
5.How does the diameter relate to the circumference of a circle?
Important Glossaries for Perimeter of Circles
- Circumference: The perimeter or total length around a circle.
- Radius: The distance from the center of a circle to any point on its boundary.
- Diameter: The distance across a circle, passing through the center; it is twice the radius.
- π (Pi): A mathematical constant approximately equal to 3.14159, used in calculations involving circles.
- Formula for circumference: The mathematical expression used to calculate the perimeter of a circle is 𝐶 = 2πr.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
