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2 <p>Last updated on<strong>September 8, 2025</strong></p>

3 <p>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.</p>

4 <h2>What is the Perimeter of a Hollow Circle?</h2>

5 <p>The perimeter<a>of</a>a hollow circle, or annulus, is the<a>sum</a>of the outer and inner circumferences of the circle.</p>

6 <p>The<a>formula</a>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.</p>

7 <p>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.</p>

8 <h2>Formula for Perimeter of Hollow Circle - 𝑷 = 2πR + 2πr.</h2>

9 <p>Let’s consider another example of a hollow circle with an outer radius R = 12 and an inner radius r = 7.</p>

10 <p>So the perimeter of the hollow circle will be: 𝑷 = 2πR + 2πr = 2π(12) + 2π(7) = 38π.</p>

11 <h2>How to Calculate the Perimeter of a Hollow Circle</h2>

12 <p>To find the perimeter of a hollow circle, apply the given formula and calculate the outer and inner circumferences separately.</p>

13 <p>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.</p>

14 <p>Example Problem on Perimeter of Hollow Circle -</p>

15 <p>For finding the perimeter, we use the formula, 𝑷 = 2πR + 2πr.</p>

16 <p>For example, let’s say R = 9 and r = 3. Now, the perimeter = 2π(9) + 2π(3) = 24π.</p>

17 <p>Therefore, the perimeter of the hollow circle is 24π.</p>

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20 <h2>Tips and Tricks for Perimeter of Hollow Circle</h2>

19 <h2>Tips and Tricks for Perimeter of Hollow Circle</h2>

21 <p>Learning some tips and tricks makes it easier to calculate the perimeter of hollow circles. Here are some tips and tricks:</p>

20 <p>Learning some tips and tricks makes it easier to calculate the perimeter of hollow circles. Here are some tips and tricks:</p>

22 <ul><li>Always remember that the perimeter of a hollow circle is the sum of its outer and inner circumferences. Use the formula, 𝑷 = 2πR + 2πr.</li>

21 <ul><li>Always remember that the perimeter of a hollow circle is the sum of its outer and inner circumferences. Use the formula, 𝑷 = 2πR + 2πr.</li>

23 </ul><ul><li>Calculating the perimeter starts by determining the radii. Make sure to measure accurately to ensure precise calculations.</li>

22 </ul><ul><li>Calculating the perimeter starts by determining the radii. Make sure to measure accurately to ensure precise calculations.</li>

24 </ul><ul><li>To reduce confusion, specifically arrange the indicated radii if you need the perimeter of<a>multiple</a>hollow circles. Apply the formula to each.</li>

23 </ul><ul><li>To reduce confusion, specifically arrange the indicated radii if you need the perimeter of<a>multiple</a>hollow circles. Apply the formula to each.</li>

25 </ul><ul><li>To avoid mistakes when adding the perimeter, ensure the radii are precise and<a>constant</a>for common uses like pipe design and mechanical components.</li>

24 </ul><ul><li>To avoid mistakes when adding the perimeter, ensure the radii are precise and<a>constant</a>for common uses like pipe design and mechanical components.</li>

26 </ul><ul><li>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.</li>

25 </ul><ul><li>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.</li>

27 </ul><h2>Common Mistakes and How to Avoid Them in Perimeter of Hollow Circle</h2>

26 </ul><h2>Common Mistakes and How to Avoid Them in Perimeter of Hollow Circle</h2>

28 <p>While working with the perimeter of a hollow circle, errors can occur. Here are some solutions to help:</p>

27 <p>While working with the perimeter of a hollow circle, errors can occur. Here are some solutions to help:</p>

29 <h3>Problem 1</h3>

28 <h3>Problem 1</h3>

30 <p>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.</p>

29 <p>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.</p>

31 <p>Okay, lets begin</p>

30 <p>Okay, lets begin</p>

32 <p>Total perimeter = 350 meters.</p>

31 <p>Total perimeter = 350 meters.</p>

33 <h3>Explanation</h3>

32 <h3>Explanation</h3>

34 <p>Let P_outer be the outer perimeter, and P_inner be the inner perimeter.</p>

33 <p>Let P_outer be the outer perimeter, and P_inner be the inner perimeter.</p>

35 <p>Given P_outer = 200 meters, P_inner = 150 meters.</p>

34 <p>Given P_outer = 200 meters, P_inner = 150 meters.</p>

36 <p>Total perimeter of the track = P_outer + P_inner = 200 + 150 = 350 meters.</p>

35 <p>Total perimeter of the track = P_outer + P_inner = 200 + 150 = 350 meters.</p>

37 <p>Therefore, the total perimeter is 350 meters.</p>

36 <p>Therefore, the total perimeter is 350 meters.</p>

38 <p>Well explained 👍</p>

37 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

38 <h3>Problem 2</h3>

40 <p>A metal ring has an outer circumference of 45 inches and an inner circumference of 30 inches. Calculate the perimeter of the hollow ring.</p>

39 <p>A metal ring has an outer circumference of 45 inches and an inner circumference of 30 inches. Calculate the perimeter of the hollow ring.</p>

41 <p>Okay, lets begin</p>

40 <p>Okay, lets begin</p>

42 <p>75 inches</p>

41 <p>75 inches</p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>Given that the outer and inner circumferences are parts of the hollow circle:</p>

43 <p>Given that the outer and inner circumferences are parts of the hollow circle:</p>

45 <p>Perimeter of the hollow ring = Outer circumference + Inner circumference = 45 + 30 = 75 inches.</p>

44 <p>Perimeter of the hollow ring = Outer circumference + Inner circumference = 45 + 30 = 75 inches.</p>

46 <p>Therefore, the perimeter of the hollow ring is 75 inches.</p>

45 <p>Therefore, the perimeter of the hollow ring is 75 inches.</p>

47 <p>Well explained 👍</p>

46 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

47 <h3>Problem 3</h3>

49 <p>Find the perimeter of a hollow circle with an outer radius of 15 cm and an inner radius of 10 cm.</p>

48 <p>Find the perimeter of a hollow circle with an outer radius of 15 cm and an inner radius of 10 cm.</p>

50 <p>Okay, lets begin</p>

49 <p>Okay, lets begin</p>

51 <p>50π cm</p>

50 <p>50π cm</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>Perimeter of the hollow circle = 2πR + 2πr P = 2π(15) + 2π(10) = 30π + 20π = 50π</p>

52 <p>Perimeter of the hollow circle = 2πR + 2πr P = 2π(15) + 2π(10) = 30π + 20π = 50π</p>

54 <p>Therefore, the perimeter of the hollow circle is 50π cm.</p>

53 <p>Therefore, the perimeter of the hollow circle is 50π cm.</p>

55 <p>Well explained 👍</p>

54 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

55 <h3>Problem 4</h3>

57 <p>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?</p>

56 <p>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?</p>

58 <p>Okay, lets begin</p>

57 <p>Okay, lets begin</p>

59 <p>64π meters of fencing is needed.</p>

58 <p>64π meters of fencing is needed.</p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>The perimeter of a hollow circle is the sum of the outer and inner circumferences.</p>

60 <p>The perimeter of a hollow circle is the sum of the outer and inner circumferences.</p>

62 <p>Using the formula: P = 2πR + 2πr P = 2π(20) + 2π(12) = 40π + 24π = 64π meters.</p>

61 <p>Using the formula: P = 2πR + 2πr P = 2π(20) + 2π(12) = 40π + 24π = 64π meters.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

63 <h3>Problem 5</h3>

65 <p>Calculate the perimeter of a hollow cylindrical pipe with an outer radius of 8 cm and an inner radius of 5 cm.</p>

64 <p>Calculate the perimeter of a hollow cylindrical pipe with an outer radius of 8 cm and an inner radius of 5 cm.</p>

66 <p>Okay, lets begin</p>

65 <p>Okay, lets begin</p>

67 <p>26π cm</p>

66 <p>26π cm</p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>The perimeter of the hollow pipe is the sum of the outer and inner circumferences.</p>

68 <p>The perimeter of the hollow pipe is the sum of the outer and inner circumferences.</p>

70 <p>P = 2πR + 2πr = 2π(8) + 2π(5) = 16π + 10π = 26π cm. The total perimeter is 26π cm.</p>

69 <p>P = 2πR + 2πr = 2π(8) + 2π(5) = 16π + 10π = 26π cm. The total perimeter is 26π cm.</p>

71 <p>Well explained 👍</p>

70 <p>Well explained 👍</p>

72 <h2>FAQs on Perimeter of Hollow Circle</h2>

71 <h2>FAQs on Perimeter of Hollow Circle</h2>

73 <h3>1.Evaluate the perimeter of a hollow circle if its outer radius is 6 cm and inner radius is 4 cm.</h3>

72 <h3>1.Evaluate the perimeter of a hollow circle if its outer radius is 6 cm and inner radius is 4 cm.</h3>

74 <p>Perimeter of hollow circle = 2πR + 2πr. Hence, P = 2π(6) + 2π(4) = 20π cm.</p>

73 <p>Perimeter of hollow circle = 2πR + 2πr. Hence, P = 2π(6) + 2π(4) = 20π cm.</p>

75 <h3>2.What is meant by the perimeter of a hollow circle?</h3>

74 <h3>2.What is meant by the perimeter of a hollow circle?</h3>

76 <p>The perimeter of a hollow circle is the total length around both the outer and inner boundaries. It is the sum of the circumferences of the outer and inner circles.</p>

75 <p>The perimeter of a hollow circle is the total length around both the outer and inner boundaries. It is the sum of the circumferences of the outer and inner circles.</p>

77 <h3>3.What are the components of a hollow circle?</h3>

76 <h3>3.What are the components of a hollow circle?</h3>

78 <p>A hollow circle, or annulus, consists of two circles: an outer circle and an inner circle, both sharing the same center but with different radii.</p>

77 <p>A hollow circle, or annulus, consists of two circles: an outer circle and an inner circle, both sharing the same center but with different radii.</p>

79 <h3>4.Which circle in a hollow circle has a larger circumference?</h3>

78 <h3>4.Which circle in a hollow circle has a larger circumference?</h3>

80 <p>The outer circle of a hollow circle always has a larger circumference than the inner circle.</p>

79 <p>The outer circle of a hollow circle always has a larger circumference than the inner circle.</p>

81 <h3>5.How can the perimeter of a hollow circle be useful in real life?</h3>

80 <h3>5.How can the perimeter of a hollow circle be useful in real life?</h3>

82 <p>The perimeter of a hollow circle is useful in designing rings, circular tracks, pipes, and various engineering and architectural applications.</p>

81 <p>The perimeter of a hollow circle is useful in designing rings, circular tracks, pipes, and various engineering and architectural applications.</p>

83 <h2>Important Glossaries for Perimeter of Hollow Circle</h2>

82 <h2>Important Glossaries for Perimeter of Hollow Circle</h2>

84 <ul><li><strong>Perimeter:</strong>The total length of the boundaries of a shape.</li>

83 <ul><li><strong>Perimeter:</strong>The total length of the boundaries of a shape.</li>

85 </ul><ul><li><strong>Hollow Circle:</strong>A shape consisting of two concentric circles, one inside the other.</li>

84 </ul><ul><li><strong>Hollow Circle:</strong>A shape consisting of two concentric circles, one inside the other.</li>

86 </ul><ul><li><strong>Radius:</strong>A line segment from the center of a circle to any point on its circumference.</li>

85 </ul><ul><li><strong>Radius:</strong>A line segment from the center of a circle to any point on its circumference.</li>

87 </ul><ul><li><strong>Circumference:</strong>The distance around the circle.</li>

86 </ul><ul><li><strong>Circumference:</strong>The distance around the circle.</li>

88 </ul><ul><li><strong>Annulus:</strong>A ring-shaped object, especially a region bounded by two concentric circles.</li>

87 </ul><ul><li><strong>Annulus:</strong>A ring-shaped object, especially a region bounded by two concentric circles.</li>

89 </ul><p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>

88 </ul><p>What Is Measurement? 📏 | Easy Tricks, Units & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math</p>

90 <p>▶</p>

89 <p>▶</p>

91 <h2>Seyed Ali Fathima S</h2>

90 <h2>Seyed Ali Fathima S</h2>

92 <h3>About the Author</h3>

91 <h3>About the Author</h3>

93 <p>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.</p>

92 <p>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.</p>

94 <h3>Fun Fact</h3>

93 <h3>Fun Fact</h3>

95 <p>: She has songs for each table which helps her to remember the tables</p>

94 <p>: She has songs for each table which helps her to remember the tables</p>