Principle of Mathematical Induction

Question

A circular wire of radius 7.5 cm is cut and bent so as to lie along the circumference of a circular hoop whose radius is 120 cm. Find, in degrees, the angle which is subtended at the centre of this hoop.

Answer

Length of the circular wire of radius 7.5 cm
Which is cut and bent = $2 πr space equals space 2 cross times straight pi cross times 7.5 space cm space equals space 15 straight pi space cm$
∴ For the circular hoop, $l italic space equals space 15 straight pi space cm comma space space space straight r space equals space 120 space cm$
Let the angle be $straight theta$ radians, Using, $l over r space equals space straight theta comma$ we have
$fraction numerator 15 straight pi over denominator 120 end fraction space equals space straight theta space space space space space space space space space space space rightwards double arrow space space space space space space space space space space space space space straight theta space equals space open parentheses straight pi over 8 close parentheses to the power of straight c space equals space open parentheses straight pi over 8 cross times 180 over straight pi close parentheses to the power of ring operator space equals space open parentheses 22 1 half close parentheses to the power of ring operator space equals space 22 degree 30 apostrophe$
Hence, the angle subtended at the centre is $22 degree 30 apostrophe.$