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

Circumference of the circle of radius 15 cm:
\[2\pi r\]
\[ = 2 \times 3 . 14 \times 15\text{ cm }\]
\[ = 94 . 2\text{ cm }\]
Now, 94.2 cm will be the length of arc

\[\left( l \right)\] for the circle with radius 120 cm.
We know: \[l = r\theta\]
\[\text{ Here,} \theta\text{ is measured in radians . }\]
\[ \therefore 94 . 2 = 120 \times \theta\]
\[ \Rightarrow \theta = 0 . 785\text{ radians }\]
45° = \[\frac{\pi}{4} = \frac{22}{7 \times 4} = 0 . 785\] radians
Therefore, the angle subtended by it at the centre of the loop is 45°.