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11

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 = 150^{o}→ 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 cm^{2}

The length of arc is 55 cm and area of sector is 577.5 cm^{2}.