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 $ $ =44\text{ }cm $ 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 $