﻿ Area Related to Circles | For Grades 9-12

# Area Related to Circles

## Area Related to Circles - Sub Topics

• What is a Circle?
• Parts of a Circle
• Ring of a Circle
• Area of a Circle
• Formulas Related to Area of a Circle
• The reading material provided on this page for Area related to Circles is specifically designed for students in grades 9 to 12. So, let's begin!

## What is a Circle?

A circle is a two-dimensional geometric shape that is perfectly round and consists of all the points in a plane that are equidistant from a fixed centre point.

## Parts of a Circle

In addition to the well-known parts of a circle such as the radius, diameter and circumference, there are other important components to be aware of. Let's explore some additional parts of a circle.

The radius of a circle is a line segment that connects the centre of the circle to any point on its circumference. It is denoted by the letter "r".

### Diameter of a Circle

The diameter of a circle is a line segment that connects two points on the circumference, passing through the centre of the circle.

### Circumference of a Circle

The circumference of a circle is the distance around its outer boundary.

Circumference = 2 π r

### Chord of a Circle

A chord is a straight-line segment that connects two points on the circumference of the circle. It does not necessarily pass through the centre.

### Tangent of a Circle

A tangent is a straight line that touches the circle at only one point, known as the point of tangency.

### Arc of a Circle

An arc is a portion of the circumference of a circle. It is measured in terms of degrees and represents a specific angle (central angle). There are two types of arcs: 1) Major arc, 2) Minor arc

### Sector of a Circle

A sector is a region enclosed by two radii of the circle and the corresponding arc between them. It is similar to a slice of a pie. There are two types of sectors: 1) Major sector, 2) Minor sector

### Segment of a Circle

A segment of a circle refers to the region bounded by an arc and the chord that connects its endpoints. There are two parts of segments:

a) Major segment b) Minor segment

## Ring of a Circle

A ring refers to the region between two concentric circles. It can be visualized as a circular band with a defined width. The outer circle represents the larger radius while the inner circle represents the smaller radius.

## Area of a Circle

The area of a circle is the amount of space inside the circle. It is calculated using the formula: A = πr2, where A is the area, π is a mathematical constant (approximately equal to 3.14) and r is the radius of the circle (the distance from the centre of the circle to its edge). The unit of measurement for the area is square units, such as square inches or square centimetres.

Example: A circle has a radius of 5 cm. Find the area of the circle.

Solution: To find the area of a circle, we use the formula

A = πr2

In this example, the radius of the circle is 5 cm, so we plug in the values and get:

A = π x 52

= 25 π           ( π = 3.14)

= 25 x 3.14

= 78.54 cm2

So, the area of the circle is 78.54 cm2.