Question -
Answer -
Find:
(i) the length of the arc
(ii) area of the sector formed by the arc
(iii) area of the segment formed by the corresponding chord
Solution
Given,
Radius = 21 cm
╬╕ = 60┬░
(i)┬аLength of an arc = ╬╕/360┬░├ЧCircumference(2╧Аr)
тИ┤ Length of an arc AB = (60┬░/360┬░)├Ч2├Ч(22/7)├Ч21
= (1/6)├Ч2├Ч(22/7)├Ч21
Or Arc AB Length = 22cm
(ii)┬аIt is given that the angle subtend by the arc = 60┬░
So, area of the sector making an angle of 60┬░= (60┬░/360┬░)├Ч╧А r2┬аcm2
= 441/6├Ч22/7 cm2
Or, the area of the sector formed by the arcAPB is 231 cm2
(iii)┬аArea of segment APB = Area of sector OAPB тАУ Area of ╬ФOAB
Since the two arms of the triangle are theradii of the circle and thus are equal, and one angle is 60┬░, ╬ФOAB is anequilateral triangle. So, its area will be тИЪ3/4├Чa2┬аsq. Units.
Area of segment APB = 231-(тИЪ3/4)├Ч(OA)2
= 231-(тИЪ3/4)├Ч212
Or, Area of segment APB = [231-(441├ЧтИЪ3)/4] cm2