Question

A circular wire of radius 1 dm is cut and is placed along the circumference of a circle of radius of one metre. The angle subtended by the wire at the centre of the circle is equal to

• A. $\frac{\pi }{4}$ radian
• B. $\frac{\pi }{3}$ radian
• C. $\frac{\pi }{5}$ radian
• D. $\frac{\pi }{10}$ radian

Answer 1

Answer: (C)

$\frac{\pi }{5}$ radian

Length of wire $=2\pi r=2\pi \times 0.1=0.2\pi m$

This length is equal to the length of the arc of the larger circle radius

$=1m$

Length of arc $=\frac{\theta }{{360}^0}\times 2\pi \times r$ (Where $\theta$ is the angle subtended at the center)

Therefore,

$\frac{\theta }{{360}^0}\times 2\pi \times 1=0.2\pi$

$\frac{\theta }{{360}^0}=0.1$

$\theta ={36}^0$

$\theta ={36}^0\times \frac{\pi }{{180}^0}$

$\theta =\frac{\pi }{5}radian$

Hence, this is the answer.