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Question

Find the radius of a circle with a central angle of 3pi/5 radians and the length of the intercepted arc equal to 6.9 cm. Round your answer to the nearest tenth.

The radius of the circle is 3.6?

Find the area of a sector with a central angle of 2pi/3radians and a radius equal to 3.4 inches. Round your answer to the nearest tenth.

The area of a sector is 12.1 inches^2.?

Answer 1

A central angle is θ = 2π/3 radians.

And radius r = 3.4 inches

Let A is area of sector

Formula: The area of sector is A = (θ/360)(πr²)

substitute  θ = 2π / 3, r = 3.4  in the equation.

A = [(2π/3) / (360)][π(3.4)²]

Recall 2π = 360

A = [(2π/3) / (2π)][π(3.4)²]

Cancel common terms

A = (1/3)[π(3.4)²]

Recall π = 3.14

A = (1/3)[(3.14)(11.56)]

A = (1/3)(36.2964)

A = 12.1

There fore

The area of sector is 12.1 inches²

Answer 2

A central angle is θ = 3π/5 radians.

And the length of the intercepted arc equal to 6.9

Arc of a circle formula: Arc length = r·θ,

Where θ is the measure of the central angle in radians and r the radius of the circle

Then r = [ Arc length/θ ]

substitute θ = 3π/5 and l = 6.9 in the equation.

radius r = (6.9) / (3π/5)

Where π = 3.14

r = (6.9) / [3(3.14)/5 ]

Simplify

r = (6.9) / [9.42/5]

r = (6.9) / (1.884)

r = 3.66242

The radius of the circle is r = 3.6