Question

A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
(a) 50°
(b) 210°
(c) 100°
(d) 60°
(e) 195°

Answer 1

(b) 210°

Length of the arc of radius = Circumference of the circle of radius 7 cm = $2\mathrm{\pi }r\mathit{=}14\mathrm{\pi }$
Now,
Angle subtended by the arc = $\frac{\mathrm{Arc}}{\mathrm{Radius}}=\frac{14\mathrm{\pi }}{12}={\left(\frac{14\mathrm{\pi }}{12}\times \frac{180}{\mathrm{\pi }}\right)}^{°}=210°$