Question

The diameter of a circle is 10 cm. Find the length of the arc, when the corresponding central angle is an given below. ($\mathrm{\pi }$ = 3.14)
(i) 144°

Answer 1

Given:
Central angle, $\mathrm{\theta }$ = 144$°$
Diameter of the circle = 10 cm
∴ Radius of the circle = $\frac{10}{2}$ cm = 5 cm
We have to find the length of the arc (l) of the circle.
We know:
Length of an arc, l = $\frac{\theta }{360}\times 2\mathrm{\pi }r$
Thus, we have:
Length of the arc, l = $\frac{144}{360}\times 2\times 3.14\times 5\mathrm{cm}$

= 12.56 cm