Question

A circular wire of radius 15 cm is cut and bent so as to lie along the circumference of a loop of radius 120 cm. Write the measure of the angle subtended by it at the centre of the loop.

Answer 1

The radius of circular wire is 15 cm.

The circumfernce of circular wire is $2\pi r=30\pi .$

The radius of loop is 120 cm.

The circumference of loop is $2\pi r=240\pi .$

The circumference of a circle covers all the quadrants of the circle i.e. the angle subtended by it at the centre is ${360}^{\circ }.$

The circular wire is cut and bent so as to lie along the circumstance of the loop. So, circumference of circular wire covers $\frac{30\pi }{240\pi }=\frac{1}{8}$ of the circumfernce of loop.

Therefore the angle subtended by the circular wire is

$\frac{{360}^{\circ }}{8}={45}^{\circ }.$