Question

The area of the minor segment of angle θ° of a circle of radius r is ___________.

Answer 1

Radius of the sector = r

Angle of the minor segment = θ

∴ Area of the minor segment = $\frac{\theta }{360°}\times \mathrm{\pi }{r}^2-r^2\sin \frac{\theta }{2}\cos \frac{\theta }{2}=\left(\frac{\theta \mathrm{\pi }}{360°}-\sin \frac{\theta }{2}\cos \frac{\theta }{2}\right)r^2$

The area of the minor segment of angle θ° of a circle of radius r is $\underline{\left(\frac{\theta \mathrm{\pi }}{360°}-\sin \frac{\theta }{2}\cos \frac{\theta }{2}\right)r^2}$.