The circumference of a circle is the distance around its boundary, much like the perimeter of any other shape. It is a key concept in geometry, particularly when dealing with circles in real-world applications such as measuring the distance traveled by wheels or calculating the boundary of round objects.
Table of Content
To calculate the circumference of a circle, we use simple formulas that involve the circle’s radius or diameter.
Here are some important terms related to circle :
| Term | Definition |
|---|---|
| Center | A fixed point related to a circle such that all points on the boundary of the circle are equidistant from it. |
| Radius | The distance from the center of the circle to any point on its circumference. |
| Chord | A line segment joining any two points on the circumference of a circle. |
| Diameter | A chord of the circle that passes through the center, also the longest chord of the circle. |
Circumference of Circle Formula
The circumference of a circle is equal to the length of its boundary, but the circle is a curved shape, its circumference can't be measured with a ruler. The correct way to find the perimeter of a circle is to calculate it using the formula C = 2π × r. If the diameter or radius of a circle is known circumference of the circle can be easily calculated.
Circumference to Diameter
The ratio of Circumference to the Diameter of a circle is always a constant and that is π. Using this fact we can calculate the formula for circumference.
Circumference/Diameter = π
Circumference = π×Diameter
Circumference to Radius
As the Diameter of a circle is two times the circle's radius, the ratio of Circumference to the radius of a circle is also always a constant, which is 2π. Using this fact we can also calculate the formula for the circumference.
Circumference/Radius =2π
Circumference = 2π×Radius
How to Find Circumference of Circle?
Perimeter of a circle is found using any of the two approach added below,
Approach 1: Due to its curved nature, directly measuring the length of a circle with a ruler or scale isn't feasible as it is for polygons like squares, triangles, and rectangles. However, you can determine the circumference of a circle using a thread. By tracing the circle's path with the thread and marking points along it, you can measure this length using a standard ruler.
Approach 2: A precise method to ascertain a circle's circumference involves calculation. To do this, the circle's radius must be known. The radius of a circle is the distance from its center to any point on its circumference. In the illustration below, a circle with radius R and center O is depicted. The diameter, twice the radius of the circle, is also shown.How to Find the Circumference of a Circle?
Circumference of Semicircle
Semicircle is the half of the circle and its image is added below,
If a circle is split into two equal parts it is called a semi-circle. The circumference of a Circle is defined as the overall length of its boundary, which is given by :
Circumference of Semi - Circle = πr + d
Where,
- r is Radius of Circle
- d is Diameter of Circle
Area of Semicircle
Area of a semi-circle is calculated by taking half of the area of the circle. i.e. the area of a semi-circle is ½ × the area of a circle. Formula for area of semi circle is given by :
Area of semi - circle = ½ × πr2
where, r is Radius of Circle
Area of Circle Formula
Area enclosed by the circumference of a circle is known as the Area of a Circle. In other words, all the area inside the boundary of the circle is considered its area and it is calculated using the formula,
A = πr2
Where,
- r is Radius of Circle
- π is Constant (π = 22/7 or 3.14)
Difference Between Circumference and Area
The differences between Area and Circumfernce between of a circle is added in the table below,
Area vs. Circumference | |
|---|---|
Area | Circumference |
Area is the measure of space occupied by the boundry of any object. | Circumference is the measure of total boundary of the figure. It is also called perimeter in shapes other than circumfernce. |
It is the measure in sq. units | It is measured in unit of length |
Related :
- Radius of Circle
- Segment of a Circle
- Equation of a Circle
- What is a Circle?
- Area of a Circle
- Sector of a Circle
Solved Examples on Circumference of Circle
Some examples on Circumference of a circle are,
Example 1: What is the circumference of a circle with a diameter of 2 cm?
Solution:
Given, diameter = 2 cm
By using formula of circumference of a circle,
C = π × d
C = 3.14 × 2
C = 6.28 cm
Example 2: What is the circumference of a circle with a radius of 3 cm?
Solution:
Given, radius = 3 cm
C = 2 × π × r
C = 2 × 3.14 × 3
C = 18.84 cm
Example 3: What is the circumference of a circle with a diameter of 14cm?
Solution:
Given, diameter = 14 cm
C = π × d
C = 3.14 × 14
C = 43.96 cm.
Example 4: What is the circumference of a circle with a radius of 10 cm?
Solution:
Given, radius = 10 cm
C = π × 2r
C = 3.14 × 2(10)
C = 62.8 cm.
Practical Applications of the Circumference of a Circle
The concept of circumference extends far beyond academic problems. In the real world, calculating the circumference helps in:
- Wheels and Gears: To determine how far a wheel or gear moves in one full rotation, we calculate the circumference. This is critical in automotive design, bike manufacturing, and machinery.
- Astronomy: Scientists often calculate the circumference of planets to better understand their size and rotation. For example, the Earth’s circumference is approximately 40,075 kilometers at the equator.
- Construction and Engineering: When building structures such as circular columns, pools, or roundabouts, the circumference is necessary for calculating material usage.
Understanding the circumference is not only a key math concept but also a practical tool in various industries.
