2
QuizMultiple Choice

Arc Length and Area of a Sector

Question 2 • Reading HS- Integrated Math I

What is the relationship between the arc length and the radius of a circle when the central angle is defined in radians?

Answer
A
The length of the arc intercepted by the central angle is equal to the radius of the circle.
B
The length of the arc intercepted by the central angle is proportional to the radius of the circle.
C
The length of the arc intercepted by the central angle is equal to the square root of the radius of the circle.
D
The length of the arc intercepted by the central angle is not related to the radius of the circle.

Explanation

For a central angle measured in radians, the arc length is given by s = rθ, where r is the radius and θ is the angle. For a fixed angle, the arc length increases in direct proportion to the radius. Therefore, the best answer is “The length of the arc intercepted by the central angle is proportional to the radius of the circle.”

AI-written and checked against the verified answer.

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