Problem preview
G-C.5 Warmup M2-033-A13-V01

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

Find arc length from a radius and central angle by converting degrees to radians when needed

Problem

In this situation, find the arc length traveled: A wheel of radius \(2~\text{feet}\) turns through \(3~\text{radians}\).

Big Picture

What this problem is really about

Circular travel is arc length: the rim point stays one radius from the center while sweeping through the given angle. Since that angle is already in radians, we’ll multiply radius by angular sweep directly and check the scale as the same fraction of a 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 central angle by converting degrees to radians when needed