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Answers
Explanation:
How To Find The Area Of A Sector Of A Circle
December 19, 2020 by Veerendra
How To Find The Area Of A Sector Of A Circle
How To Find The Area Of A Sector Of A Circle 1
If the arc subtends an angle of θ at the centre, then its arc length is
θ 180 × π r
Hence, the arc length ‘l’ of a sector of angle θ in a
circle of radius r is given by
l= θ 180 × π r ……. (i)
If the arc subtends an angle θ, then area of the corresponding sector is
πr2θ360
Thus, the area A of a sector of angle θ in a circle of radius r is given by
A= θ360 × π r2
=θ360 × (Area of the circle) …….. (ii)
= × (Area of the circle) ….(ii)
Some useful results to remember:
(i) Angle described by minute hand in 60 minutes = 360º
Angle described by minute hand in one minute
=(36060)0= 6o
Thus, minute hand rotates through an angle of 6º in one minute.
(ii) Angle described by hour hand in 12 hours = 360º
Angle described by hour hand in one hour
=(36012)0=30o
In a circle with radius r and centre at O, let ∠POQ = θ (in degrees) be the angle of the sector. Then, the area of a sector of circle formula is calculated using the unitary method. Now the area of the sector for the above figure can be calculated as (1/8) (3.14×r×r).