Question

What is the shaded portion of the figure?

Answer 1

D

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 =
`(112)/(360) \pi (6)^(2) \\=(56)/(5) \pi cm^(2)`

Next we will find the area of FAE.

Radius of FAE = AE = 4cm

Area of FAE =
`(112)/(360) \pi (4)^(2) \\=(224)/(45) \pi cm^(2)`

Lastly,

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

=
`(56)/(5) \pi -(224)/(45)\pi \\=(56)/(9) \pi cm^(2)`

Therefore the answer is D.