Question

Find the area the sector.arc circle 9A. 275π/6 m²B. 175π/2 m²C. 18π m²D. 5π/3 m²

Answer 1

Solution:

The area of a sector is expressed as

$\begin{gathered} area=\frac{\theta}{360}\times\pi r^2 \\ where \\ \theta\Rightarrow angle\text{ subtended by the sector} \\ r\Rightarrow radius\text{ of the circle} \end{gathered}$

Given:

we see that

$\begin{gathered} \theta=165\degree \\ r=10\text{ m} \end{gathered}$

By substitution, we have

$\begin{gathered} area=\frac{165}{360}\times\pi\times10\times10 \\ =\frac{275\pi}{6}\text{ m}^2 \end{gathered}$

Hence, the area of the sector is evaluated to be

$\frac{275\pi}{6}\text{ m}^2$

The correct option is A