Question

The minor arc formed by two radii subtending an angle of $50$ degree at the center of a circle is $20$ cm in length. Find the radius of the circle.
Take $\pi =3.14$

• A. $48.56cm$
• B. $22.93cm$
• C. $45.86cm$

Answer 1

The correct option is B $22.93cm$

Length of the arc $=20cm$
Angle subtended at the center $\theta =50$ degree
$⟹20=\frac{\theta }{360}\times \pi \times d$, where $d$ is the diameter of the circle.

$⟹20=\frac{50}{360}\times 3.14\times d$

$⟹20\times \frac{36}{5}=3.14\times d$

$⟹20\times \frac{36}{5}\times \frac{1}{3.14}=d$

$⟹4\times 36\times \frac{1}{3.14}=d$

$⟹d=\frac{144}{3.14}$

$⟹d=45.859=45.86cm$

$\therefore$ Radius of the circle $=\frac{d}{2}=\frac{45.86}{2}=22.93cm$


Option (b.) is correct.