Introduction
The two radii of the central angle θ and the formation of the arc in between the points on the circle which forms the sector of a circle .The sector of a circle is nothing but the calculation of a part of the whole area of the circle. The angles in the circle which can be measured in degrees or radians.
Let us take the angle θ of the circle to be the central angle and the total area circle is given as πr2.In this the 2π is the angle for the whole part of the circle.
Formula for the Sector of Circle:
Formula: The area of a sector of circle:
Area = `(theta pi R^2)/360`
Where, C is the central angle in degrees,
R is the radius of the circle
π is Pi, approximately 3.142
The formula is obtained by taking the area of a whole circle, and then a fraction of it which depends on the central angle is the area of sector. In the sector of the circle, if the central angle is 90°, then the sector of the circle will have some portion which is equal to one quarter of the whole circle..
When the central angle is in radians, then the formula for area of the sector can be given as,
Area=R2C/2
Where, C is the central angle in radians and
R is the radius of the circle of which the sector is part.
Example for Sector of Circle:
Ex 1: The sector of a circle consists of radius 8 cm and angle 40°.Find the area of the sector of a circle and also the major part of the circle.
Sol:
Area of sector = `theta/360` × πr2
= `40/360` × 3.14 × 64
= 22.34 cm2
Thus, the area of the major circle = area of circle – area of minor circle.
= 50.2 – 22.34
= 27.86 cm2
Ex 2: If the radius of the circle is equal to the value of 12 inches and the central angle is 1500. Solve the area of the sector of a circle.
Sol:
The given values are r = 12 inches and `theta` = 1500
Area:
Area of a sector is solved through the following formula,
A=` (theta)/(360^0)` x π r2
That is A= `(150^0) / (360^0) ` x 3.14 x 12 x 12
Simplifying this we have to get
A= 10800 square inches.
This is the area of the arc of a sector.
Stuck on any of these topics how to do substitution method, solve this math problem for me try out some best math website like mathsisfun,and math dot com.
Ex 3: If the radius of the circle is 5 cm and the central angle is 1470. Solve the area of the sector of a circle.
Sol:
The given values are r = 5 cm and theta = 1470
Area:
Area of a sector is solved through the following formula,
A= `(theta)/(360^0)` x π r2
That is A= `(147^0) / (360^0)` x 3.14 x 5 x 5
Simplifying this we have to get
A= 1837.5 square cm.
This is the area of the arc of a sector.
The two radii of the central angle θ and the formation of the arc in between the points on the circle which forms the sector of a circle .The sector of a circle is nothing but the calculation of a part of the whole area of the circle. The angles in the circle which can be measured in degrees or radians.
Let us take the angle θ of the circle to be the central angle and the total area circle is given as πr2.In this the 2π is the angle for the whole part of the circle.
Formula for the Sector of Circle:
Formula: The area of a sector of circle:
Area = `(theta pi R^2)/360`
Where, C is the central angle in degrees,
R is the radius of the circle
π is Pi, approximately 3.142
The formula is obtained by taking the area of a whole circle, and then a fraction of it which depends on the central angle is the area of sector. In the sector of the circle, if the central angle is 90°, then the sector of the circle will have some portion which is equal to one quarter of the whole circle..
When the central angle is in radians, then the formula for area of the sector can be given as,
Area=R2C/2
Where, C is the central angle in radians and
R is the radius of the circle of which the sector is part.
Example for Sector of Circle:
Ex 1: The sector of a circle consists of radius 8 cm and angle 40°.Find the area of the sector of a circle and also the major part of the circle.
Sol:
Area of sector = `theta/360` × πr2
= `40/360` × 3.14 × 64
= 22.34 cm2
Thus, the area of the major circle = area of circle – area of minor circle.
= 50.2 – 22.34
= 27.86 cm2
Ex 2: If the radius of the circle is equal to the value of 12 inches and the central angle is 1500. Solve the area of the sector of a circle.
Sol:
The given values are r = 12 inches and `theta` = 1500
Area:
Area of a sector is solved through the following formula,
A=` (theta)/(360^0)` x π r2
That is A= `(150^0) / (360^0) ` x 3.14 x 12 x 12
Simplifying this we have to get
A= 10800 square inches.
This is the area of the arc of a sector.
Stuck on any of these topics how to do substitution method, solve this math problem for me try out some best math website like mathsisfun,and math dot com.
Ex 3: If the radius of the circle is 5 cm and the central angle is 1470. Solve the area of the sector of a circle.
Sol:
The given values are r = 5 cm and theta = 1470
Area:
Area of a sector is solved through the following formula,
A= `(theta)/(360^0)` x π r2
That is A= `(147^0) / (360^0)` x 3.14 x 5 x 5
Simplifying this we have to get
A= 1837.5 square cm.
This is the area of the arc of a sector.
