Additional Mathematics – Circular measure | e-Consult

Answer 2

The area A of a sector is A = \frac{1}{2}r^{2}\theta.

With r = 8 cm and \theta = \frac{\pi}{4}:

\[

A = \frac{1}{2}\times 8^{2}\times\frac{\pi}{4}

= \frac{1}{2}\times 64\times\frac{\pi}{4}

= 32\times\frac{\pi}{4}

= 8\pi\text{ cm}^{2}

\]

Hence the sector area is \(\displaystyle 8\pi\) cm².