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Find the area of the shaded reigon

Find the area of the shaded reigon-example-1

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Answer:

40π/3 cm^2 ≈ 41.89 cm^2

Explanation:

The centerline of the shaded region has a radius of 3cm+(4 cm)/2 = 5 cm. Its length is 1/3 that of the circumference of a circle with that radius (because 120° is 1/3 of 360°).

The area is the product of the centerline length and the width of the shaded area (4 cm).

shaded area = (1/3)(2π(5 cm))(4 cm)

shaded area = 40π/3 cm^2 ≈ 41.89 cm^2

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Alternate solution

The area of the donut is the difference in the areas of the outer and inner circles:

πr₂² -πr₁² = π((7 cm)^2 -(3 cm)^2) = 40π cm^2

The are of the shaded region is (120°/360°) = 1/3 of that, so is

shaded area = (40/3)π cm^2

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