Answer:
D
Step-by-step explanation:
Area of Part of a Circle = (θ/360)[tex]\pi r^{2}[/tex]
We first find the area of CAB first.
Radius of CAB = AB = 6cm
θ = 112
Area of CAB = [tex]\frac{112}{360} \pi (6)^{2} \\=\frac{56}{5} \pi cm^{2}[/tex]
Next we will find the area of FAE.
Radius of FAE = AE = 4cm
Area of FAE = [tex]\frac{112}{360} \pi (4)^{2} \\=\frac{224}{45} \pi cm^{2}[/tex]
Lastly,
Area of Shaded Region = Area of CAB - Area of FAE
= [tex]\frac{56}{5} \pi -\frac{224}{45}\pi \\=\frac{56}{9} \pi cm^{2}[/tex]
Therefore the answer is D.
