Calculate the length of an arc of a circle with a radius of 8 cm if this arc has a degree measure of 110 °.

univerkov | April 14, 2021 | education

Determine the circumference of a circle with a radius of 8 cm.

L = 2 * n * R = 2 * n * 8 = 16 * n cm.

The full circle is 3600, then the arc AB is 110/360 = 11/36 part, and the length of the arc is 11/36 part of the circumference.

Then Larc = 11 * L / 36 = 11 * 16 * p / 36 = 15.4 cm.

You can also use the ready-made arc length formula:

L = n * R * α / 180 = n * 8 * 110/180 = 15.4 cm.

Answer: The length of the arc is 15.4 cm.

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