Question

In the given figure, the radius of the circle is 7 cm and m ( arc MBN) = 60^°,

find  A(O - MCN). 

Answer 1

Radius of the circle, r = 7 cm
m(arc MBN) = ∠MON = θ = 60º

Area of Sector `= theta/360^\circ xx pir^2`

`60/360 xx pixx7^2`

`1/6 xx pixx49`

`=(49pi)/6 cm^2`

`(49xx22)/(6xx7)`

`1078/42`

≈ 25.67 cm²

Since angle ∠MON = 60^∘ and OM = ON = radius = 7 cm

`Area = 1/2 r^2 sin(theta)`

`1/2 xx 7xx7xxsin(60^\circ)`

`=49/2xxsqrt3/2`

`=(49sqrt3)/4`

`= (49xx1.732)/4`

`=84.868/4`

≈ 21.22 cm²

= Area of Sector OMN − Area of Triangle OMN

= 25.67 − 21.22

= 4.45 cm^2​