Question

Select the correct answer.What is the area of the shaded portion of the figure? Express your answer in terms of pi.О А.OB.O C.O D.AF56k5657π72845722445112EAE = 4 cmBAB= 6 cm

Answer 1

Given the figure of two circles with the same center A

We will find the area of the shaded portion

The area of the shaded portion = the difference between the area of the sectors opposite the central angle of 112

The area of the sector opposite the angle θ =

$\frac{\theta}{360}*\pi r^2$

The radius of the larger circle = AB = 6 cm

The radius of the smaller circle = AE = 4 cm

So, the area of the shaded portion =

$\begin{gathered} \frac{\theta}{360}*\pi *(AB^2-AE^2) \\ \\ =\frac{112}{360}*\pi *(6^2-4^2) \\ \\ =\frac{112}{360}*\pi *(36-16)=\frac{112*20}{360}\pi=\frac{56}{9}\pi \end{gathered}$

So, the answer will be option A. 56/9 π