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A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π.

a) 84/7π
b) 56/7π
c) 120/7π
d) 96/7π

User Cuadraman
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1 Answer

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Final answer:

The arc length of a circle with a 21-inch radius and a central angle of 4π/7 radians is 84/7π inches, option a.

Step-by-step explanation:

The question asks to calculate the length of an arc in a circle with a radius of 21 inches, intercepted by a central angle of 4π/7 radians. To find the arc length, we use the formula:

arc length (s) = radius (r) × central angle (θ)

Since the radius of the circle (r) is 21 inches and the central angle (θ) is 4π/7 radians, we can plug these values into the formula to find the arc length:

s = 21 inches × (4π/7)

By multiplying these values, we get:

s = (21 × 4π/7) inches

Simplifying the expression:

s = (84π/7) inches

Therefore, the correct answer is 84/7π inches, which corresponds to option a.

User Vijayinani
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