Question

A circular wire of radius 1 dm is cut and is placed along the circumference of a circle of radius of one meter 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

The correct option is C $\frac{\pi }{5}$radian

The radius of wire is 1 dm=$\frac{1}{10}$m

Then circumference of wire =$2\times \pi \times \frac{1}{10}=\frac{\pi }{5}$M

Then circumference of wire= length of are of circle

$\therefore \frac{\pi }{5}=\frac{\theta }{360}\times \left(2\pi \right(1\left)\right)$

$\Rightarrow \theta =\frac{{180}^0}{5}=\frac{\pi }{5}$ Rediun