Circle is one of the easy-grasping topics of geometry , you may observe circular shapes around you. Having an understanding of circular geometry can be of greater importance as we sometimes deal with the problems related to circular objects in our daily lives.
In this article we have brought you combined information that includes fundamentals of Circle, perimeter, area , Area of a sector of Circle and length of a arc of the circle.so let's first begin with the basics of Circle next the topics we have listed above.
What is Circle
Circle is the locus of points (a group of points) that are at equal distance from a fixed point and that fixed point is called the centre of the circle.
Diameter : Diameter is a straight line on the circle that connects any two points on the circle and passes through the centre of Circle.It is generally denoted by (D) or (d).
Here the length \( AB \) in the Diagram called the diameter of the circle
Radius : Radius is the length that is exactly half of the diameter of a circle Or It is defined as the fixed distance From the centre to any point on the locus of Circle and it is denoted by (R) or (r).
Radius = \( D \over 2 \)
Perimeter and Area of the Circle
Perimeter/ Circumference : The total length that is required to form the boundary of a circle is called Perimeter
The perimeter of a circle is calculated by the following formula:
\( Perimeter = 2\pi R \)
Semi - Perimeter : Half of the perimeter of Circle.
The semi- perimeter of a circle is
= \( \pi R \)
Area of the circle
Area : The area of a circle is the space that is occupied by it .
Area of the circle= \( \pi R^2 \)
Area of the Semi- Circle is given by:
= \( {\pi R^2}\over 2\)
Sector and Segment of a Circle
Sector : A Sector is the area bounded between two radii and an arc of the circle.
Minor Sector : Area bounded between two radii and a minor arc is called minor Sector.
Major Sector : Area bound between two radii and a major arc is called major Sector.
Area of the sector = \( {\theta\over 360°}\pi R^2\)
Where \(\theta\) is the angle subtended by the arc at the centre.
Length of an Arc = \( {\theta\over 360°}2\pi R\)
Perimeter of a Sector : Arc length+ 2R
Segment : A Segment is the area bounded between a chord and an arc of a circle.
Minor Segment: Area bounded between a chord and a minor arc of the circle.
Major Segment: Area bounded between a chord and a major arc of the circle.
Solved Examples for Sector and Segment of a Circle
Example 1 : An arc subtends an angle of 30° at the centre of a circle of radius 7 cm. Find the areas of the minor and major sectors
Ans : Radius of the circle = 7 cm
Angle subtended by arc \(\theta\) = 30°
Area of the the minor Sector = \( {\theta\over 360°}\pi R^2\)
= \( {30°\over 360°}\times {22 \over7 }\times 7^2\)
= 12.83 \( cm^2 \)
Area of the Major sector = Area of the circle- Area of the minor Sector
Area of the circle = \( \pi R^2\)
= \( {22\over 7}\times 7^2\)
= \( 22 \times 7\)
=154 \(cm^2\)
Area of the Major sector = \(154-12.83 \)
= 141.16 \(cm^2\)
Tags
Circle Basics