Question

Find the area of the shaded sector of the circle . The area of the shaded sector is_ m2(Simplify your answer . Type an exact answer in terms of pi.)

Answer 1

In order to calculate the area of the yellow sector, first we need to know that the area of the complete circle (360°) is given by:

$A=\pi r^2$

Also, the radius of this circle is 7, since the diameter is 14 and the radius if half the diameter.

Then, we can use the following rule of three:

$\begin{gathered} \pi r^2\to360\degree \\ x\to110\degree \\ \\ \frac{\pi r^2}{x}=\frac{360}{110} \\ \frac{\pi\cdot7^2}{x}=\frac{36}{11} \\ 36x=49\pi\cdot11 \\ x=\frac{539\pi}{36} \end{gathered}$

So the area is 539π/36.