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G-C.5 Warmup M2-033-A04-V01

Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.

Find arc length from a radius and a central angle measured in radians

Problem

Find arc length for radius \(6\) and central angle \(\pi/3~\text{radians}\).

Unworked sector or circular-context diagram showing only supplied givens. Open full size
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What this problem is really about

Since the angle is already in radians, arc length follows the direct scaling relationship without a degree conversion. We’ll keep pi exact, multiply the radius by the angular measure, and check the result against the same fraction of the full circumference.

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Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.5
Category
Geometry
Domain
Circles
Objective
Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.
Problem type
Find arc length from a radius and a central angle measured in radians