In the figure, O is the centre of the circle.
m(arc PQR)`=60^@`
OP = 10 cm.
Find the area of the shaded region. `(pi=3.14,sqrt3=1.73)`

Answer

`9.08 cm^2`

Explanation

The radius of the circle ( r) = OP = 10 cm
m(arc PQR)`=theta= 60^@`
The shaded region is segment PQR.
A(segment PQR) `= r^2[(pitheta)/360-(sintheta)/2]`
`=10^2[(3.14xx60)/360-sin60/2]`
`=100[3.14/6-sqrt3/(2xx2)]...[:'sin60=sqrt3/2]`
`100xx[3.14/6-1.73/4]...( :'sqrt3=1.73)`
`=100[(3.14xx2-1.73xx3)/12]`
`=100[(6.28-5.19)/12]`
`=100xx1.09/12=109/12`
`=9.083~~9.08 cm^2`