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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

What is the area of the shaded portion of the circle? A: (16pi-32) in^2 B: (16pi-8) in-example-1

1 Answer

5 votes

Answer:

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

User Rimon
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