 ## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 11 of Exercise 18B

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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 = 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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