Question

The diameter of a circle is $10$ cm, then find the length of the arc, when the corresponding central angle is ${144}^{\circ }$.$(\pi =3.14)$

• A. $44$ cm
• B. $12.56$ cm
• C. $12$ cm
• D. $88$ cm

Answer 1

The correct option is B $12.56$ cm

Radius of the circle $=\frac{Diameter}{2}=5cm$
Length of an arc subtending an angle $\theta =\frac{\theta }{360}\times 2\pi R$ where $R$ is the radius of the circle.

So, length of the arc $=\frac{144}{360}\times 2\times 3.14\times 5cm$

$=\frac{144}{360}\times 31.7cm$

$=12.56cm$