Question

A circle has a radius of 12. 6 cm. What is the exact length of an arc formed by a central angle measuring 120°? Enter your answer in the box. Express your answer using π. Cm.

Answer 1

Any smooth curve connecting two places is called an arc. The length of the arc is 26.3894 cm.

What is an arc?

Any smooth curve connecting two places is called an arc. The arc length is the measurement of how long an arc is. A graph arc is an ordered pair of neighbouring vertices in a graph.

What is the length of the arc?

The length of the arc that is making an angle of θ, at the centre of the arc is given by the formula,

$\text{Length of the arc}=2\pi r \times \dfrac{\theta}{360^o}$

As it is given that the measure of the angle at the centre of the circle is 120°, while the radius of the circle is 12.6 cm. therefore, the length of the arc,

$\text{Length of the arc}=2\pi r \times \dfrac{\theta}{360^o}$

Substitute the values,

$\text{Length of the arc}=2\pi \times 12.6 \times \dfrac{120^o}{360^o}$

                            $= 26.3894\rm\ cm$

Hence, the length of the arc is 26.3894 cm.

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