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Find the area of the shaded sector. Round your answer to the nearest hundredth

Find the area of the shaded sector. Round your answer to the nearest hundredth-example-1

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Answer:

(a) 65.85 km²

Explanation:

You want the area of a sector with radius 7 km and central angle 154°.

Area

The formula for the area of a sector is ...

A = 1/2r²θ . . . . where r is the radius and θ is the central angle in radians

Application

A = 1/2(7 km)²(154·π/180) ≈ 65.85 km²

The area of the shaded sector is about 65.85 square km.

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Additional comment

The last two answer choices can be eliminated because their units are distance units, not area units.

The area of the circle is πr², about 154 km². The shaded part is less than half, but somewhat more than 1/7, so will be less than 77 and more than 22 km². For this problem, a rough estimate of the area can tell you which is the reasonable answer choice.

Find the area of the shaded sector. Round your answer to the nearest hundredth-example-1
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