Lengths of Arcs

The measure of an arc is given in degrees.  The length of an arc depends on the size of the circle and is measured in standard units, such as inches, centimeters, etc.  The circumference of a circle is an arc measuring 360^o.  The length of the circumference is given by the formula:  C = πd, where d is the diameter of the circle.  This formula can also be given as:  C = 2πr, where r is the radius.  An arc measuring θ degrees is θ /360 of the circumference, so its length can be found by either of these formulas:

or

Example 1:  Find the length of a 72^o arc in a circle of radius 10 cm.

Solution: 

length = 72/360 Χ 20π = 4π cm or about 12.57 cm

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