A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of the arc and the area of the sector.
Consider the circle shown above,
Given radius of the circle = R = 21 cm → eqn1
And angle of the sector = θ = 150o→ eqn2
Length of arc of a sector
Where ‘R’ = radius of sector (or circle)
θ = angle subtended by the arc on the centre of the circle
Put the values of R and θ from equation 1 and 2 in equation 3
= 138600/2520
= 55 cm
Area of a sector
Where ‘R’ = radius of sector (or circle)
θ = angle subtended by the arc on the centre of the circle
Put the values of R and θ from equation 1 and 2 in equation 3
= 1455300/2520
= 577.5 cm2
The length of arc is 55 cm and area of sector is 577.5 cm2.
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