Question

The diameter of a circle is $10$ cm. Find the length of the arc, in cm, (nearest integral value), when the corresponding central angle is ${45}^{\circ }$.

Answer 1

Radius of the circle $=\frac{\text{Diamete}r}{2}=5$ cm
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 $=\frac{45}{360}\times 2\times \frac{22}{7}\times 5=3.93$ cm

Answer to nearest integer is $4$ cm.