Question

The figure shows a quadrant of a circle centre O and radius 15 cm. Q is a point on the arc PR such that

Arc PQ : Arc QR = 4 : 3.
If Angle QOR = x radians
Calculate
i) the value of x

ii) the area of the shaded region

Answer 1

Part a

`\angle POR=(\pi)/(2)` radians, so
`\theta=(3)/(7)(\pi/2)=\boxed{(3\pi)/(14)}`

Part b

The area of sector QOR is
`(1)/(2)(15^2)\left((3\pi)/(14) \right)=(675\pi)/(28)`

The area of triangle POQ is
`(1)/(2)(15)(15) \sin (2\pi)/(7)=(225)/(2) \sin (2\pi)/(7)`

So, the total area, in square centimeters, is
`(675\pi)/(28)+(225)/(2) \sin (2\pi)/(7)`