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

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

Part b

The area of sector QOR is $\frac{1}{2}(15^2)\left(\frac{3\pi}{14} \right)=\frac{675\pi}{28}$

The area of triangle POQ is $\frac{1}{2}(15)(15) \sin \frac{2\pi}{7}=\frac{225}{2} \sin \frac{2\pi}{7}$

So, the total area, in square centimeters, is $\frac{675\pi}{28}+\frac{225}{2} \sin \frac{2\pi}{7}$