Question

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

• A. $50{}^{\circ }$
• B. $210{}^{\circ }$
• C. $100{}^{\circ }$
• D. $60{}^{\circ }$
• E. $30{}^{\circ }$

Answer 1

Answer: (B)

Length of wire $=2\pi r=2\times \frac{22}{7}\times 7$ $=44cm$ Let $\theta$ be the angle subtended by an arc at the centre. $\therefore$ $44=\frac{22}{7}\times \frac{2\times 12\times \theta }{360{}^{\circ }}$ $\Rightarrow$ $\theta =\frac{44\times 7\times 360{}^{\circ }}{22\times 2\times 12}$ $=210{}^{\circ }$