Question

Find the area of the sector of a circle of radius $14units$ subtended by an angle of $\frac{23\pi }{12}\mathrm{radians}$. Round your answer to the nearest tenth, and do not include the units in your answer.

Answer 1

Finding the area of the sector of the circle:

A_sector = $\frac{Angleofsector}{\left(2\mathrm{\pi }\right)}\left(\mathrm{\pi }\right)\left({\mathrm{r}}^2\right)$

Substituting the value of $r$

A_sector = $\frac{{\displaystyle \frac{23\mathrm{\pi }}{12}}}{\left(2\pi \right)}\left(\pi \right){14}^2$

A_sector = $\frac{23}{24}(\mathrm{\pi }\times {14}^2)$

Substituting and solving

A_sector = $\frac{23}{24}(\pi \times 196)=\frac{4508\mathrm{\pi }}{24}=\frac{1127\mathrm{\pi }}{6}\approx 590.1$

Hence the area of the sector is $590.1$.