# Given circle o with minor arc AB= 60 degrees and OA= 12. What is the area of sector AOB?

Mar 19, 2018

Area $= \frac{24}{5} \pi \textcolor{w h i t e}{. .} \leftarrow \text{ Exact answer}$

Area $= 15.08 {\text{ units}}^{2}$ to 2 decimal places$\leftarrow \text{ Approximation}$

#### Explanation:

Let the area of the sector be $a$

Circumference of a circle is $\pi D \Leftrightarrow 2 \pi r$

So the circumference of the whole circle is $2 \pi 12 = 24 \pi$

But we only have ${60}^{o}$ worth of that circle

So as a fraction of the whole circle it is $\frac{60}{360} \equiv \frac{6}{30} \equiv \frac{1}{5}$

So the area of the sector is:

$a = \frac{1}{5} \times 24 \pi = \frac{24}{5} \pi \textcolor{w h i t e}{. .} \leftarrow \text{ Exact answer}$

$a = 15.0796447 \ldots \ldots$

$a = 15.08 {\text{ units}}^{2}$ to 2 decimal places$\leftarrow \text{ Approximate area}$