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Finding length of arc or area of sector given radius only

Finding length of arc or area of sector given radius only. Length of the arc =. x Circumference of circle. Central angle of sector. Central angle of sector. The length of an arc is equal to ratio of central angle(Ɵ) of the sector to central

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Finding length of arc or area of sector given radius only

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  1. Finding length of arc or area of sector given radius only

  2. Length of the arc = x Circumference of circle Central angle of sector Central angle of sector The length of an arc is equal to ratio of central angle(Ɵ) of the sector to central angle of the circle(3600) multiplied by the circumference of the circle. Central angle of circle Central angle of circle ∴ Length of the arc = Ɵ Ɵ The area of an arc is equal to ratio of central angle(Ɵ) of the sector to central angle of the circle(3600) multiplied by the area of the circle. Area of the arc = x area of circle ∴ Area of the arc =

  3. Another formula for area of sector We know that area of sector This can also be written as, (By splitting πr2 as ) (By taking out) Length of arc (l) Area of sector given radius and length of arc (l) =

  4. Example 1: Find the area of the sector if length of the arc is 48 m and radius is 10 m Solution: Given: Length of arc (l) = 48 m Radius of circle (r) = 10 m To find: Area of sector When the length of the arc and radius is given, we can directly find the area of sector using the formula given below. Area of sector 24 = 24 x 10 = 240 m2 Ans: Area of sector = 240m2

  5. Example 2: Find the length of the arc if area of sector is 462cm2 and radius of the circle is 21 cm. Solution: Given: Area of sector (A) = 462 cm2 , Radius of the circle (r) = 21 cm To find: Length of the arc (l) We know that area of sector (A) = To find length of arc (l), we need to transpose ‘2’ and radius (r) to the other side. We get, 22 154 A = 462 and r = 21 7 l = 2 x 22 = 44 Ans: Length of arc (l) = 44 cm

  6. Try These Q1) Find the length of the arc if area of sector is 231cm2 and radius of the circle is 14 cm. Q2) Find the area of the sector if length of the arc is 96 m and radius is 20 m.

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