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 substended by the arc at the centre is

• A. ${50}^{\circ }$
• B. ${210}^{\circ }$
• C. ${100}^{\circ }$
• D. ${60}^{\circ }$
• E. ${195}^{\circ }$

Answer 1

The correct option is B

${210}^{\circ }$

Length of the arc of radius

= Circumference of the circle of radius 7 cm

$=2\pi r=14\pi$

Now,

Angle subtended by the arc

$=\frac{\text{Arc}}{\text{Radius}}=\frac{14\pi }{12}$

$={(\frac{14\pi }{12}\times \frac{180}{\pi })}^{\circ }={210}^{\circ }$