Radian Measure Math Example 2

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Example 2

medium
A wheel of radius 55 cm rotates through an angle of 2.42.4 radians. Find the arc length and the area of the sector swept.

Solution

  1. 1
    Arc length: s=rθ=5×2.4=12s = r\theta = 5 \times 2.4 = 12 cm.
  2. 2
    Sector area: A=12r2θ=12(25)(2.4)=30A = \frac{1}{2}r^2\theta = \frac{1}{2}(25)(2.4) = 30 cm².
  3. 3
    These formulas work directly in radians. In degrees one would need an extra π/180\pi/180 factor, illustrating why radians are natural for circular motion.

Answer

Arc length =12= 12 cm; Sector area =30= 30 cm²
Radian measure makes circular geometry formulas elegant: arc length s=rθs=r\theta and sector area A=12r2θA=\frac{1}{2}r^2\theta hold without any conversion factor. This is the key practical advantage of radians.

About Radian Measure

An angle measure defined by the arc length subtended on a unit circle: one radian is the angle that subtends an arc equal in length to the radius.

Learn more about Radian Measure →

More Radian Measure Examples

Example 1 easy

Convert [formula] to radians and [formula] radians to degrees. Show the conversion steps.

Example 3 easy

Convert: (a) [formula] to radians, (b) [formula] to radians, (c) [formula] to degrees, (d) [formula]

Example 4 medium

A clock's minute hand is [formula] cm long. How far does its tip travel in [formula] minutes? How la

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