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102 LearnersLast updated on September 8, 2025
Perimeter of Hollow Circle
The perimeter of a shape is the total length of its boundary. In the context of a hollow circle, also known as an annulus, the perimeter consists of the outer and inner circumferences. Perimeter calculations are essential in various applications, such as engineering, architecture, and design. In this topic, we will learn about the perimeter of a hollow circle.
What is the Perimeter of a Hollow Circle?
The perimeter of a hollow circle, or annulus, is the sum of the outer and inner circumferences of the circle.
The formula for the perimeter of a hollow circle is 𝑷 = 2πR + 2πr, where R is the radius of the outer circle and r is the radius of the inner circle.
For instance, if a hollow circle has an outer radius R = 10 and an inner radius r = 6, then its perimeter is 𝑷 = 2π(10) + 2π(6) = 32π.
Formula for Perimeter of Hollow Circle - 𝑷 = 2πR + 2πr.
Let’s consider another example of a hollow circle with an outer radius R = 12 and an inner radius r = 7.
So the perimeter of the hollow circle will be: 𝑷 = 2πR + 2πr = 2π(12) + 2π(7) = 38π.
How to Calculate the Perimeter of a Hollow Circle
To find the perimeter of a hollow circle, apply the given formula and calculate the outer and inner circumferences separately.
For instance, if a hollow circle has an outer radius R = 8 and an inner radius r = 5, the perimeter is: Perimeter = 2π(8) + 2π(5) = 26π.
Example Problem on Perimeter of Hollow Circle -
For finding the perimeter, we use the formula, 𝑷 = 2πR + 2πr.
For example, let’s say R = 9 and r = 3. Now, the perimeter = 2π(9) + 2π(3) = 24π.
Therefore, the perimeter of the hollow circle is 24π.
Tips and Tricks for Perimeter of Hollow Circle
Learning some tips and tricks makes it easier to calculate the perimeter of hollow circles. Here are some tips and tricks:
- Always remember that the perimeter of a hollow circle is the sum of its outer and inner circumferences. Use the formula, 𝑷 = 2πR + 2πr.
- Calculating the perimeter starts by determining the radii. Make sure to measure accurately to ensure precise calculations.
- To reduce confusion, specifically arrange the indicated radii if you need the perimeter of multiple hollow circles. Apply the formula to each.
- To avoid mistakes when adding the perimeter, ensure the radii are precise and constant for common uses like pipe design and mechanical components.
- If you know the difference in the radii, you can calculate the approximate perimeter increase or decrease when adjusting the size of the hollow circle.
Common Mistakes and How to Avoid Them in Perimeter of Hollow Circle
While working with the perimeter of a hollow circle, errors can occur. Here are some solutions to help:
Mistake 1
Incorrectly using the area formula for circles instead of the perimeter formula.
Remember that the perimeter is the sum of the circumferences, not the area. Use 𝑷 = 2πR + 2πr.
Mistake 2
Confusing the terms 'radius' and 'diameter', leading to incorrect calculations.
Ensure you are using the radius (half of the diameter) in the perimeter formula. The radius is essential for accurate calculations.
Mistake 3
Assuming that the inner and outer circles have the same radius, which results in inaccurate calculations.
A hollow circle has different radii for the inner and outer circles. Ensure you differentiate between them for accurate calculations.
Mistake 4
Using the wrong values for the radii, misreading a problem, or mislabeling the radii.
Double-check the problem and ensure you're using the correct radii for your hollow circle.
Mistake 5
Misunderstanding or misidentifying the radii given in a problem outline.
Before starting the calculations, make sure you understand the problem and, if possible, try to sketch the hollow circle to accurately identify the radii.
Perimeter of Hollow Circle Examples
Problem 1
A circular racetrack has an outer perimeter of 200 meters and an inner perimeter of 150 meters. To find the total perimeter of the track, sum the outer and inner perimeters.
Total perimeter = 350 meters.
Explanation
Let P_outer be the outer perimeter, and P_inner be the inner perimeter.
Given P_outer = 200 meters, P_inner = 150 meters.
Total perimeter of the track = P_outer + P_inner = 200 + 150 = 350 meters.
Therefore, the total perimeter is 350 meters.
Problem 2
A metal ring has an outer circumference of 45 inches and an inner circumference of 30 inches. Calculate the perimeter of the hollow ring.
75 inches
Explanation
Given that the outer and inner circumferences are parts of the hollow circle:
Perimeter of the hollow ring = Outer circumference + Inner circumference = 45 + 30 = 75 inches.
Therefore, the perimeter of the hollow ring is 75 inches.
Problem 3
Find the perimeter of a hollow circle with an outer radius of 15 cm and an inner radius of 10 cm.
50π cm
Explanation
Perimeter of the hollow circle = 2πR + 2πr P = 2π(15) + 2π(10) = 30π + 20π = 50π
Therefore, the perimeter of the hollow circle is 50π cm.
Problem 4
A hollow circular garden has an outer radius of 20 meters and an inner radius of 12 meters. How much fencing is needed to enclose both the outer and inner boundaries?
64π meters of fencing is needed.
Explanation
The perimeter of a hollow circle is the sum of the outer and inner circumferences.
Using the formula: P = 2πR + 2πr P = 2π(20) + 2π(12) = 40π + 24π = 64π meters.
Problem 5
Calculate the perimeter of a hollow cylindrical pipe with an outer radius of 8 cm and an inner radius of 5 cm.
26π cm
Explanation
The perimeter of the hollow pipe is the sum of the outer and inner circumferences.
P = 2πR + 2πr = 2π(8) + 2π(5) = 16π + 10π = 26π cm. The total perimeter is 26π cm.
FAQs on Perimeter of Hollow Circle
1.Evaluate the perimeter of a hollow circle if its outer radius is 6 cm and inner radius is 4 cm.
2.What is meant by the perimeter of a hollow circle?
3.What are the components of a hollow circle?
4.Which circle in a hollow circle has a larger circumference?
5.How can the perimeter of a hollow circle be useful in real life?
Important Glossaries for Perimeter of Hollow Circle
- Perimeter: The total length of the boundaries of a shape.
- Hollow Circle: A shape consisting of two concentric circles, one inside the other.
- Radius: A line segment from the center of a circle to any point on its circumference.
- Circumference: The distance around the circle.
- Annulus: A ring-shaped object, especially a region bounded by two concentric circles.
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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
