Question

In a circle of diameter $40cm$, the length of a chord is $20cm$, then the length of minor arc of the chord is

• A. $\frac{20\pi }{7}cm$
• B. $\frac{\pi }{3}cm$
• C. $\frac{10\pi }{3}cm$
• D. $\frac{20\pi }{3}cm$

Answer 1

Answer: (D)

Since, diameter of the circle $=40cm$
$\therefore$ Radius of the circle $(r)=20cm$
and length of the chord $(l)=20cm$
From the shown figure, it is clear that $\angle AOB=60^{\circ }=\frac{\pi }{3}$ radian

$\therefore$ Length of minor arc of the chord $(l)=$ radius of circle $(r)\times$ angle subtended in radian by the minor arc $(\theta )$
$=20\times \frac{\pi }{3}=\frac{20\pi }{3}cm$