Question

A circular wire of radius $7$ cm is cut and bend again into an arc of a circle of radius $12$ cm. The angle subtended by the arc at the centre is

• A. ${50}^{\circ }$
• B. ${210}^{\circ }$
• C. ${100}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

Answer: (B)

${210}^{\circ }$

Given that diameter of circular wire $=14$ cm
Therefore, length of circular wire $=14\pi$ cm
$\therefore$ Required angle $=\frac{\text{arc}}{\text{radius}}$

$=\frac{14\pi }{12}=\frac{7\pi }{6}=\frac{7}{6}\pi .\frac{{180}^o}{\pi }={210}^o$