Arc Length

Presentation

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Mathematics

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9th - 12th Grade

•

Practice Problem

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Medium

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CCSS

HSG.C.B.5

Standards-aligned

Yessenia Rivera

Used 482+ times

FREE Resource

7 Slides • 7 Questions

Arc Length

Objectives

Recognize the formulas for finding the arc length given degrees or radians.
Calculate a sector's arc length

Definition

Arc Length: the section of the circumference of a circle between 2 radii.
Arc length measured using radians.

Kinds of Arcs

Minor Arc: Arc created by an angle of $180\degree$ / $\pi$ radians or less
Major Arc: Arc created by an angle or more than $180\degree$ / $\pi$ radians
Semicircular Arc: Arc created when both angles are equal

Formula for Arc Length

If we begin with Degrees: $\frac{\pi}{180}r\theta$
If we begin with Radians $r\theta$

Example

Find the length of the blue arc given the radius of the circle is 8 cm, and the angle measure shown is in radians. Give the answer to one decimal place.

Multiple Choice

Find the arc length indicated by the bolded arc.

8.3 in

7.2 in

6.8 in

6.4 in

Multiple Choice

Find the arc length indicated by the bolded arc.

17.3 km

79.1 km

95.0 km

99.0 km

Multiple Choice

Find the arc length indicated by the bolded arc.

8.4 mi

9.4 mi

60.2 mi

117.8 mi

Example

A pendulum of length 26 cm swings $58\degree$ . Find the length of the circular pathway that the pendulum makes giving the answer in centimetres in terms of 𝜋.

Multiple Choice

Find the arc length of the bolded arc.

Multiple Choice

Find the length of the bold arc. Leave $\pi$ in your answer.

5688π ft

15.8π ft

150.4π ft

54,150 ft

Multiple Choice

The formula for the arc length given an angle measurement in degrees is

$\frac{\pi}{180}r\theta$

$\frac{\pi}{360}r\theta$

$\pi r^2$

Multiple Choice

The formula for the arc length given an angle measurement in radians is

$2\pi r\theta$

$r^2$

$r\theta$

Arc Length

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