Sectors of Circle

A minor sector is formed by the smaller central angle at the centre (less than \(180^\circ\)).

It covers the smaller region enclosed by the two radii.

A major sector is formed by the larger central angle (greater than \(180^\circ\)).

It covers more than half of the circle.

When the central angle is exactly \(180^\circ\), the sector becomes a semicircle.

The fraction of the entire circle represented by the sector is:

\(\dfrac{\theta}{360^\circ}\)

\(\text{Area of Sector} = \dfrac{\theta}{360^\circ} \times \pi r^2\)

Radius \(r = 7\text{ cm}\) and central angle \(\theta = 60^\circ\):

\(A = \dfrac{60}{360} \times \pi \times 7^2 = \dfrac{1}{6} \times 49\pi = \dfrac{49\pi}{6}\text{ cm}^2\)

\(\text{Arc Length} = \dfrac{\theta}{360^\circ} \times 2\pi r\)

For \(r = 10\text{ cm}\), \(\theta = 72^\circ\):

\(L = \dfrac{72}{360} \times 2\pi \times 10 = \dfrac{1}{5} \times 20\pi = 4\pi\text{ cm}\)