Question

What is the shaded portion of the figure?

Answer 1

Answer:

D

Step-by-step explanation:

Area of Part of a Circle = (θ/360)$\pi r^{2}$

We first find the area of CAB first.

Radius of CAB = AB = 6cm

θ  = 112

Area of CAB = $\frac{112}{360} \pi (6)^{2} \\=\frac{56}{5} \pi cm^{2}$

Next we will find the area of FAE.

Radius of FAE = AE = 4cm

Area of FAE = $\frac{112}{360} \pi (4)^{2} \\=\frac{224}{45} \pi cm^{2}$

Lastly,

Area of Shaded Region = Area of CAB - Area of FAE

= $\frac{56}{5} \pi -\frac{224}{45}\pi \\=\frac{56}{9} \pi cm^{2}$

Therefore the answer is D.