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 =

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

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