Question

What is the area of the shaded portion of the circle?

A: (16pi-32) in^2
B: (16pi-8) in^2
C: (64pi- 32) in^2
D: (64pi - 8) in^2

Answer 1

1st option

Explanation:

the area of the shaded portion is calculated as

area of sector - area of white Δ

area of sector = area of circle × fraction of circle

= πr² ×
`(90)/(360)` ( r is the radius )

= π × 8² ×
`(1)/(4)`

= 64π ×
`(1)/(4)`

= 16π in²

area of Δ =
`(1)/(2)` bh ( b is the base and h the perpendicular height )

here b = h = 8

area of Δ =
`(1)/(2)` × 8 × 8 =
`(1)/(2)` × 64 = 32 in²

then

area of shaded portion = (16π - 32 ) in²