radius of sector of circle is 21cm If length of arc of that sector is 55 cm find the area of the sector
Answers
Answer:
The area of the sector = 577.5 cm^2
Step-by-step explanation:
It is given that radius of circle = 21cm
length of arc of that sector is 55 cm
The ratio arc length of sector to circumference of circle is same as ratio of area of sector to area of circle
arc length/ circumference = 55/(2πr)
The area of sector is 55/(2πr)of total area of circle with radius 21cm
To find area of circle with radius 21cm
Area = πr^2
To find the area of sector
Area of sector =(55/2pr)xπr^2=55r/2 = (55 x 21)/2 = 577.5 cm^2
Therefore sector area = 577.5 cm^2
Answer:
Area of sector is 577 cm²
Step-by-step explanation:
Given that
Radius of sector of circle = r = 21 cm
Lenght of arc of sector =l= 55 cm
We have to find
Area of Sector = A =?
As we know
Area of sector = A = r²θ/2 = 0.5r²θ.....(A
Lets first find theta (θ)
We know that
length of arc = radius of arc x central angle of arc
l = rθ
θ = l/r
θ = 55/21
Now substitute the value of θ in equation A along with the value of radius
A = 0.5(21)² x 55/21
A= 577.5 cm²
So, the area of sector is 577.5 cm²