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129 LearnersLast updated on December 11, 2025
Perimeter of a Circle with Diameter
The perimeter of a shape is the total length of its boundary. In the case of a circle, the perimeter is known as the circumference. The diameter of the circle is used to calculate this perimeter. Perimeter is useful for tasks such as fencing a circular area, sewing circular patterns, and more. In this topic, we will learn about the perimeter of a circle using the diameter.
What is the Perimeter of a Circle with Diameter?
The perimeter of a circle, also known as the circumference, is the total length around the circle.
The formula for the circumference of a circle using its diameter is C = pi x d, where d is the diameter of the circle.
For example, if a circle has a diameter of 12 cm, then its circumference is C = pi x 12 = 37.68 cm (using pi approx 3.14).
Formula for Perimeter of a Circle - \( C = \pi \times d \)
Let’s consider another example of a circle with a diameter of 20 cm.
So the perimeter of the circle will be: C = pi x 20 = 62.8 cm (using pi approx 3.14).
How to Calculate the Perimeter of a Circle
To find the perimeter of a circle, we use the formula C = pi x d, where d is the diameter of the circle.
For instance, if a given circle has a diameter of 15 cm, the perimeter is C = pi x 15 = 47.1 cm (using pi approx 3.14).
Example Problem on Perimeter of a Circle - For finding the perimeter of a circle with a given diameter, we use the formula C = pi x d .
For example, if the diameter is 25 cm, the perimeter = pi x 25 = 78.5 cm (using pi approx 3.14).
Therefore, the circumference of the circle is 78.5 cm.
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Tips and Tricks for Perimeter of a Circle
Learning some tips and tricks makes it easier for children to calculate the perimeter of circles.
Here are some tips and tricks given below:
Always remember that a circle's perimeter, or circumference, is calculated using the formula C = pi x d.
Calculating the perimeter of a circle starts by determining the diameter. If the radius is given, remember that the diameter is twice the radius.
To reduce confusion, specifically, keep the value of pi consistent, usually using pi approx 3.14 for easier calculations unless a more precise value is needed.
To avoid mistakes when calculating the circumference, ensure the diameter is measured accurately for common uses like gardening and architecture.
If you are given the circumference and need the diameter, you can rearrange the formula to d = C / pi.
Common Mistakes and How to Avoid Them in Perimeter of a Circle
Did you know that while working with the perimeter of a circle, children might encounter some errors or difficulties? We have solutions to resolve these problems.
Here are some given below:
Mistake 1
Incorrectly using the formula for circumference, confusing it with area formulas.
Remember that the formula for circumference is C = pi x d, not the area formula A = pi x r2.
Mistake 2
Students may confuse the concepts of radius and diameter, leading to incorrect calculations.
It is important to note that the diameter is twice the radius, and the circumference is calculated using the diameter.
Mistake 3
Assuming that any rounded number for pi is acceptable, which results in inaccurate calculations.
While pi approx 3.14 is commonly used for simplicity, using a more precise value like pi approx 3.14159 can yield more accurate results.
Mistake 4
Using the wrong values for the diameter, misreading a problem, or mislabeling the diameter and radius.
Double-check the problem and ensure that you're using the correct diameter for your circle.
Mistake 5
Misunderstanding or misidentifying the diameter when only the radius is given.
Before starting the calculations, make sure you understand the problem, and remember that the diameter is twice the radius.
Perimeter of a Circle Examples
Problem 1
A circular garden has a diameter of 10 meters. To find the perimeter, which is the circumference of the garden, use the formula \( C = \pi \times d \).
31.4 meters
Explanation
Given diameter d = 10 meters.
Circumference of the circle = C = pi x d = 3.14 x 10 = 31.4 meters. Therefore, the perimeter of the garden is 31.4 meters.
Problem 2
A circular track has a diameter of 15 meters. Find the length around the track using the formula for circumference.
47.1 meters
Explanation
Given diameter d = 15 meters.
Circumference of the circle = C = pi x d = 3.14 x 15 = 47.1 meters. Therefore, the length around the track is 47.1 meters.
Problem 3
If a circle has a diameter of 22 cm, what is its circumference?
69.08 cm
Explanation
Circumference of the circle = C = pi x d = 3.14 x 22 = 69.08 cm. Therefore, the circumference of the circle is 69.08 cm.
Problem 4
A circular pool is being designed with a diameter of 8 meters. How much fencing is needed to go around the pool?
25.12 meters
Explanation
The circumference of the circle is the total length around it.
Using the formula: C = pi x d = 3.14 x 8 = 25.12 meters. Therefore, 25.12 meters of fencing is needed to go around the pool.
Problem 5
Find the circumference of a circle with a diameter of 5 meters.
15.7 meters
Explanation
The circumference of the circle = C = pi x d = 3.14 x 5 = 15.7 meters. Therefore, the circumference of the circle is 15.7 meters.
FAQs on Perimeter of a Circle
1.Evaluate the circumference if the diameter of a circle is 6 cm.
2.What is meant by a circleโs perimeter?
3.What are the units used for circumference?
4.What is the relationship between diameter and radius?
5.Why is \( \pi \) used in calculating circumference?
Important Glossaries for Perimeter of a Circle
- Circumference: The total length around a circle.
- Diameter: The distance across a circle through its center.
- Radius: The distance from the center of the circle to any point on its boundary.
- Pi (pi): A constant used in calculations involving circles, approximately equal to 3.14.
- Formula of circumference: The mathematical expression used to calculate the perimeter of a circle is C = pi x d.
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
