Question

A piece of wire 20 cm long is bent into the form of an arc of a circle of radius ${\displaystyle \frac{60}{\pi }}$ cm. The angle subtended by the arc at the centre of the circle is ______.

Options

• 30°

• 60°

• 90°

• 50°

Answer 1

A piece of wire 20 cm long is bent into the form of an arc of a circle of radius ${\displaystyle \frac{60}{\pi }}$ cm. The angle subtended by the arc at the centre of the circle is 60°.

Explanation:

Given:

• Length of the wire = 20 cm
• Radius of the circle = ${\displaystyle \frac{60}{\pi }}$

s = rθ

${\displaystyle 20=\left(\frac{60}{\pi }\right)\theta }$

${\displaystyle \theta =\frac{20\pi }{60}}$

${\displaystyle \theta =\frac{\pi }{3}}$ radius

1 radian = ${\displaystyle \frac{180°}{\pi }}$

${\displaystyle \theta =\frac{\pi }{3}\times \frac{180°}{3}}$

= 60°