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105 LearnersLast updated on September 26, 2025
Perimeter of Hollow Cylinder
The perimeter of a shape refers to the total length of its boundary. In the case of a hollow cylinder, it is the measurement around the outer and inner circles. This concept is used in various applications such as construction and manufacturing. In this topic, we will explore the perimeter of a hollow cylinder.
What is the Perimeter of a Hollow Cylinder?
The perimeter of a hollow cylinder consists of the outer and inner circular boundaries.
To find the perimeter, you calculate the circumference of both circles. The formula for the circumference of a circle is πͺ = 2ππ, where π is the radius.
For a hollow cylinder with an outer radius R and inner radius r , the total boundary length is the sum of both circumferences: P = 2πR + 2πr
For instance, if the outer radius is 6 and the inner radius is 4, the perimeter is P = 2π(6) + 2π(4) = 20π .
Formula for Perimeter of Hollow Cylinder - P = 2πR + 2πr .
Let’s consider another example of a hollow cylinder with an outer radius R = 8 and an inner radius r = 6 . The perimeter of the hollow cylinder will be: P = 2πR + 2πr = 2π(8) + 2π(6) = 28π .
How to Calculate the Perimeter of a Hollow Cylinder
To find the perimeter of a hollow cylinder, apply the formula and calculate the circumference of both the outer and inner circles. For example, a hollow cylinder has an outer radius R = 10 and an inner radius r = 7
The perimeter is the sum of the circumferences, P = 2πR + 2πr = 2π(10) + 2π(7) = 34π . Example Problem on Perimeter of Hollow Cylinder - To find the perimeter of a hollow cylinder, use the formula, P = 2πR + 2πr
. For example, if R = 5 and r = 3 then the perimeter is 2π(5) + 2π(3) = 16π . Therefore, the perimeter of the hollow cylinder is 16π.
Tips and Tricks for Perimeter of Hollow Cylinder
Learning some tips and tricks makes it easier to calculate the perimeter of hollow cylinders. Here are some tips:
- Always remember that the perimeter of a hollow cylinder is the sum of the circumferences of the outer and inner circles. Use the formula, P = 2πR + 2πr .
- To avoid confusion, clearly distinguish between the outer radius R and the inner radius r .
- Double-check your calculations to ensure accuracy, especially in practical applications like construction and engineering.
- If you are given the diameter instead of the radius, remember the relationship Diameter= 2 xRadius.
- Use precise values for π (e.g., 3.14 or 22/7) to ensure accurate calculations in practical scenarios.
Common Mistakes and How to Avoid Them in Perimeter of Hollow Cylinder
Did you know that while working with the perimeter of a hollow cylinder, people might encounter some errors or difficulties? We have solutions to resolve these problems. Here are some given below:
Mistake 1
Confusing the radius and diameter when calculating circumference.
Remember that the circumference formula uses the radius, not the diameter. The radius is half the diameter.
Mistake 2
Forgetting to include both the outer and inner circumferences in the total perimeter calculation.
Ensure that both the outer and inner circle circumferences are included by using the formula \( P = 2πR + 2πr \).
Mistake 3
Using incorrect values for π, leading to inaccurate results.
Use standardized values for π, such as 3.14 or 22/7, for precise calculations.
Mistake 4
Mixing up the outer and inner radii.
Double-check the problem and ensure that you correctly identify and use the outer and inner radii.
Mistake 5
Misreading or mislabeling the given dimensions.
Before starting calculations, carefully read the problem and, if possible, sketch the hollow cylinder to accurately identify the dimensions.
Perimeter of Hollow Cylinder Examples
Problem 1
A cylindrical pipe has an outer radius of 10 cm and an inner radius of 8 cm. What is the perimeter of the hollow cylinder?
36π cm
Explanation
Let R be the outer radius and r the inner radius.
Given R = 10 cm and r = 8 cm.
Perimeter of hollow cylinder = 2πR + 2πr .
P = 2π(10) + 2π(8) = 20π + 16π = 36π cm.
Therefore, the perimeter is 36π cm.
Problem 2
A hollow metal tube is being used in a construction project. The tube has an outer radius of 15 inches and an inner radius of 12 inches. Calculate the perimeter of the hollow cylinder.
54π inches
Explanation
Given that the outer radius R = 15 inches and inner radius r = 12 inches: Perimeter = 2πR + 2πr
P = 2π(15) + 2π(12) = 30π + 24π = 54π inches.
Therefore, the perimeter of the hollow cylinder is 54π inches.
Problem 3
Find the perimeter of a hollow cylinder with an outer radius of 9 cm and an inner radius of 5 cm.
28π cm
Explanation
Perimeter of hollow cylinder = 2πR + 2πr . P = 2π(9) + 2π(5) = 18π + 10π = 28π cm. Therefore, the perimeter is ( 28π cm.
Problem 4
A hollow cylinder is used as a pillar in a building, with an outer radius of 20 meters and an inner radius of 18 meters. What is the total perimeter of this hollow cylinder?
76π meters
Explanation
The perimeter of a hollow cylinder is the sum of the circumferences of the outer and inner circles. Using the formula:
P = 2πR + 2πr .
P = 2π(20) + 2π(18) = 40π + 36π = 76π meters.
Problem 5
Calculate the perimeter of a hollow pipe with an outer radius of 11 cm and an inner radius of 7 cm.
36π cm
Explanation
Find the total distance around the pipe by summing the circumferences of both circles
Perimeter = 2πR + 2πr . P = 2π(11) + 2π(7) = 22π + 14π = 36π cm.
FAQs on Perimeter of Hollow Cylinder
1.Evaluate the perimeter of a hollow cylinder if its outer radius is 4 cm and inner radius is 2 cm.
2.What is meant by the perimeter of a hollow cylinder?
3.What are the applications of calculating the perimeter of a hollow cylinder?
4.Which measurement is used in the perimeter formula of a hollow cylinder?
5.How do you determine the diameter from the radius in a hollow cylinder?
Important Glossaries for Perimeter of Hollow Cylinder
- Perimeter: The total boundary length of a shape.
- Hollow Cylinder: A 3D shape with two concentric circles at the top and bottom.
- Circumference: The distance around a circle, calculated as 2πr .
- Outer Radius: The radius from the center to the outer boundary of the cylinder.
- Inner Radius: The radius from the center to the inner boundary of the cylinder.
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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
