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Home » Circles » Arcs, Angles, and Sectors » Arc Length Formula

Arc Length Formula

Last updated: Mar 27, 2021 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

In today's lesson, we will show a simple formula for finding the length of an arc in a circle.

An arc is a part of the circle's circumference. A circle measures 360°, so the length of an arc that is the entire circle (an arc measuring 360°)  is simply the circle's circumference, given by C=2*π*r.

A partial arc will have a length that is the same proportion of the circumference as the arc's measure in degrees is of 360°. The length of an arc measuring 90° will be a quarter of the circumference, the length of an arc measuring 45° will be an eighth of the circumference, and so on.

In general, for an arc measuring θ°, the arc length s, is s= 2*π*r*θ/360.

Problem

A CD has an area of 17.35 square inches. Find the length of a 60° arc.

Geometry: arc in a circle

Strategy

A circle is entirely defined by its radius - so we can get the radius of the CD from its area. Once we have the radius, we will use the above formula (s= 2*π*r*θ/360) to find the arc length.

Solution

ACD=17.35
Acircle= π*r2
r2=17.35/π=5.5225
r=√5.5225=2.35

s= 2*π*r*θ/360= 2*π*2.35*60/360=2.46 inches

« Circles: Finding the Area of a Ring
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About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected].

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Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

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