Table of Contents
Introduction
The distance along the boundary of a circle is the Circumference of the circle. In other words, it is the total length of the boundary.
For example, if an athlete starts at a point on a circular track, then, the distance he covers around the track to reach the same point again is the circumference of the track.
Definition and Formula of Circumference
The circumference formula is used to calculate the distance around the edge or boundary of a circle. It is expressed as:
Circumference = 2 x π x r
or
C = 2πr
where:
Circumference (C) is the distance around the edge of the circle, measured in units such as meters (m) or centimeters (cm).
π (pi) is a mathematical constant approximately equal to 3.14159 (often rounded to 3.14).
r is the radius of the circle, which is the distance from the center of the circle to any point on its edge.
The formula states that the circumference of a circle is equal to twice the product of π and the radius of the circle. The radius is multiplied by 2π because π represents the ratio of the circumference to the diameter of a circle and multiplying it by the radius gives the circumference directly.
This formula is widely used in geometry, trigonometry, and various fields of science and engineering where circles are involved. It allows for the calculation of the circumference of a circle based on its radius or vice versa.
Solved Examples on Circumference Formula:
Example 1: Finding the circumference when the radius is given
Given: Radius (r) = 5 cm
To find: Circumference (C)
Using the circumference formula: C = 2πr
C = 2 x 3.14 x 5
C ≈ 31.4 cm
Therefore, when the radius is 5 cm, the circumference of the circle is approximately 31.4 cm.
Example 2: Finding the radius when the circumference is given
Given: Circumference (C) = 12 m
To find: Radius (r)
Using the circumference formula: C = 2πr
12 = 2 x 3.14 x r
12 = 6.28r
r ≈ 1.91 m
Therefore, when the circumference is 12 m, the radius of the circle is approximately 1.91 m.
Example 3: Finding the circumference when the diameter is given
Given: Diameter (d) = 10 cm
To find: Circumference (C)
First, we need to find the radius using the formula:
radius = diameter / 2
r = 10 cm / 2 = 5 cm
Using the circumference formula: C = 2πr
C = 2 x 3.14 x 5
C ≈ 31.4 cm
Therefore, when the diameter is 10 cm, the circumference of the circle is approximately 31.4 cm.
Frequently Asked Question on Circumference Formula:
1: What is the Circumference of a Circle?
Answer: The circumference of a circle is the distance around the outer boundary or edge of the circle. It is the total length of the curve that forms the circle. The circumference is directly related to the size of the circle and can be found using the formula:
Circumference = 2 x π x r
where:
- Circumference (C) is the distance around the circle.
- π (pi) is a mathematical constant approximately equal to 3.14159 (often rounded to 3.14).
- r is the radius of the circle, which is the distance from the center of the circle to any point on its edge.
2: How to Calculate Diameter from Circumference?
Answer: To calculate the diameter of a circle when the circumference is known, you can use the following formula:
Diameter = Circumference / π
or
d = C / π
where:
Diameter (d) is the distance across the circle, passing through its center.
Circumference (C) is the distance around the circle.
π (pi) is a mathematical constant approximately equal to 3.14159 (often rounded to 3.14).
3: What are the steps involved in finding the circumference of a circle if its area is given?
Answer: To find the circumference of a circle when its area is given, you can follow these steps:
- Determine the formula for the area of a circle: The formula for the area of a circle is A = π r2, where A represents the area and r is the radius of the circle.
- Rearrange the formula to solve for the radius: r = √(A / π) In this step, take the square root of (A / π) to find the radius.
- Calculate the circumference using the radius: Circumference = 2 πr Substitute the value of the radius into the formula to find the circumference.
By following these steps, you can find the circumference of a circle when its area is given.
4: What is the value of pi?
Answer: The value of pi (π) is a mathematical constant representing the ratio of a circle’s circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a simple fraction or a finite decimal. Pi is approximately equal to 3.14159, but its decimal representation goes on infinitely without repeating.
5: Which formula is used to find the perimeter of a circle, when its area is given?
Answer: To find the perimeter (circumference) of a circle when its area is given, you need to use the following formula:
Perimeter = 2 x √(π x Area)
where:
- Perimeter refers to the circumference of the circle.
- π (pi) is a mathematical constant approximately equal to 3.14159 (often rounded to 3.14).
- Area represents the given area of the circle.
The formula calculates the perimeter by taking the square root of the product of π and the area, and then multiplying it by 2.
6: What are the units of circumference?
Answer: Since a circle’s circumference is the linear distance of the circle’s edge, it describes a length. Therefore, the most common units of a circle’s circumference are millimeter, centimeter, meter for the metric system, and inch, feet, and yard for the imperial system.
7: How do you find the circumference of a 1m circle?
Answer: To calculate the circumference of a circle with a radius of 1 meter, simply follow these steps: Multiply the radius by 2 to get the diameter of 2 meters. Multiply the result by π, or 3.14 for an estimation. And there you go; the circumference of a circle with a radius of 1 meter is 6.28 meters.
8: How to Calculate Diameter from Circumference?
Answer: The formula for circumference = diameter × π
Or, diameter = circumference/π
So, the diameter of the circle in terms of circumference will be equal to the ratio of the circumference of the circle and pi.
9: Find the circumference of a circle in terms of π, if the radius measures 3 cm.
Answer: We know that,
Circumference = 2πr = 2π(3) = 6π
Therefore, the circumference of a circle is 6π cm, if its radius is 3 cm.
