The formula of the perimeter of circle is implemented to find out the perimeter of the circle. So, what do you mean by the perimeter of the circle? The perimeter of the circle means the boundary which is enclosed by the boundary or the arc length of the circle. The term which signifies the perimeter of a specific circle is known as the ‘circumference of the circle’. Thus, if we study the perimeter of the circle, it is implied that we are also studying the circumference of the circle as well.

## Formula of Perimeter of Circle

The perimeter of the circle consists of three components – 2 constants and one variable which represents the radius of the circle. Thus, the formula of the perimeter of the circle is:

2 π r = π D units

In this case, r is termed as the radius of the circle, and D is denoted as the diameter of the circle.

## Example

**Example:** Utilizing the formula for the perimeter of the circle, calculate the circumference of the circle which have a diameter of 8 cm. (consider the value of π as 22/7)

**Solution:**

Find the perimeter of the Circle:

Diameter of the Circle = 8 cm.

The formula for the perimeter of the circle = π D

Perimeter = 22/7 X 8 = 25.14 cm.

Thus, the Perimeter of the Circle is 25.14 cm.

## Diameter of a Circle

We have studied in our earlier classes, a circle is a two-dimensional space where there are many collected points that are centered at an equidistance from the center of the circle. Thus, the distance from the center located at any point on the surface of the circle is called ‘radius’. Thus with this concept will arise the concept of diameter which is the point from one end of the circle passing the center point to the other point of the circle.

From another point, we can say that diameter is twice the length of the radius of the circle.

Thus, the longest chord in a circle is its diameter. The diameter can be written as ‘d’, ‘φ’, ‘D’, ‘Dia’.

## Properties of a Diameter

The properties of a diameter are listed:

- The diameter is known as the longest chord of any circle.
- The diameter will divide the circle into two equal parts and thereby will produce two identical semi-circles.
- The mid-point of the diameter locates the center of the circle which is known as the radius of the circle.
- The radius is half of the diameter.

These were two contracted learning of the circle – The formula of the circumference of the circle and the diameter of the circle. The content was an intent study on these two topics particularly. The students can study this content for revision purposes or for preliminary understanding of the concept. For the full-fledged study, the students are required to practice sums related to the formula of the perimeter of the circle.

## Formula of Diameter of Circle

There are many ways to calculate the diameter of a circle. The ways are as follows:

- If the radius of the circle is known then – D = 2R
- If the circumference of the circle is known then – D = C/π ( where C is the circumference and π has a constant value which is 22/7 or 3.14)
- When the area of the circle is known then – the formula which will help us to calculate the circle is – D=4Aπ or D=2Aπ (in this case A is the area of the circle)

Consecutively, if the students want to know in-depth or study other mathematical concepts they can visit Cuemath to book a free session.