Question

A circle with radius $3$ has a sector with a central angle of $60°$. What is the area of the sector?

Answer 1

Find the area of the circular sector based on given information:

We know that the area of sector is given by $\frac{\mathrm{\theta }}{360°}{\mathrm{\pi r}}^2$, where $\mathrm{\theta }$ is the angle of sector and $\mathrm{r}$ is the radius of circle.

So, area of sector with $\mathrm{\theta }=60°$ and $\mathrm{r}=3$ units is;

$\mathrm{A}=\frac{60°}{360°}\mathrm{\pi }{\left(3\right)}^2$

$\Rightarrow$$\mathrm{A}=\frac{1}{6}\left(3.14\right)\left(9\right)[\because \mathrm{\pi }=3.14]$

$\Rightarrow$$\mathrm{A}=4.71$ square units

Hence, area of sector is $4.71$square units.