An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc
Question 1 Report
An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc
Answer Details
When an angle in degrees is subtended at the center of a circle, the length of the arc it cuts out is given by:
$$\text{Length of arc} = \frac{\text{angle}}{360^\circ} \times 2\pi r$$
where r is the radius of the circle.
In this case, the angle is 60° and the radius is 3 cm. Substituting these values into the formula above, we get:
$$\text{Length of arc} = \frac{60}{360^\circ} \times 2\pi (3\text{ cm}) = \frac{1}{6} \times 6\pi = \pi \text{ cm}$$
Therefore, the length of the arc, in terms of π, is π cm.
Hence, the correct option is: \(\pi\)cm.
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