Åk 6–9

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3.3 Circle Arcs
 A circle arc is part of the circle’s edge. Circle Arc, Radius, Central Angle On page 2.3 in this section, we learned to calculate the circumference of a circle.  Here, we will learn how to calculate the length of a circle’s arc.  In order to calculate the length of a circle’s arc, we need to know its central angle and radius.

A central angle is created when you draw two radii in a circle.

By using the central angle size, we can find out how large of a potion of the circle’s circumference is covered. The whole circle contains 360o.

By dividing the central angle for the circle sector which the circle arc covers by 360o we get how large of a portion of the total circle is covered.

In order to calculate the circle sector’s length, we compare the circle arc’s portion with the circle’s total circumference. The formula looks like this:

Example 1

How long is the circle arc in the figure?

 c = 85o 360o · p · 2 · 6 ≈ 8.9 cm

We can also calculate the central angle’s size if we know the circle arc’s length and the circle’s radius.

Example 2

How large is the central angle in this figure?

 v 360o · p · 2 · 4 = 7 cm

1. We multiply by 360o on both sides.

 v · 360o 360o · p · 2 · 4 = 7 · 360o

v · p · 2 · 4 = 2,520

1. We divide by p, with 2, and with 4 on both sides.

 v · p · 2 · 4 p · 2 · 4 = 2,520 p · 2 · 4

 v = 2,520 p · 2 · 4 ≈100o