Question

In a circle of radius 21cm, an arc subtends an angle 60 degree at the centre. Find


(i) the length of the arc (ii) area of the sector formed by the arc

(iii)area of the line segment formed by the corresponding chord.

Answer 1

area = ( theta/360)×pi.radius^2
area=(60/360)×(22/7)×21×21
area= 11×21=231cm^2

length of arc= (60/360)×2pi.r
=1/6×22/7×2×21=22cm

area of corresponding chord=area of sector- area of triangle(equilateral)
area of triangle formed = 1/2× base×height
hence 2 sides of triangle is equal so 2x+60=180
2x=120
x=60
so this become equilateral traingle
nd height is denoted by √3/2×side
so height=√3/2×21cm
so area of traingle is 1/2×√3/2×21×21=441√3/4
hence area of segment=231-441√3/4 cm^2