Question

The figure shows a circle with centre O and radius 4cm. \(\angle\) BOD = \(72^\circ\). A point is selected at random inside the circle. Find the probability that point lies inside the sector.

Answer 1

Area of circle
= $\pi$$\times$${\left(4cm\right)}^2$
= 16$\pi$${cm}^2$
Sector is subtending an angle of ${72}^{\circ }$.
$\therefore$ area of sector is

= $\frac{72}{360}$$\times$area of circle

= $\frac{1}{5}$$\times$area of circle

Hence area of sector = $\frac{16}{5}$$\pi$${cm}^2$

$\therefore$ Probability, P(point lies inside the sector)

= $\frac{\frac{16}{5}\pi }{16\pi }$

= $\frac{1}{5}$