Question

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

Answer 1

Length of circular wire of radius $7.5$cm

which is cut and bent$=2\pi r=2\times \pi \times 7.5=15\pi$cm

$\therefore$ For circular hoop

$l=15\pi$cm; $r=120$cm.

Let the angle between be ${}^{\prime }{\theta }^{\prime }$ radians, using $\frac{l}{r}=\theta$

$\frac{15\pi }{120}=\theta$

$\Rightarrow \theta =\frac{\pi }{8}$

$\theta =\frac{\pi }{8}\times \frac{180}{\pi }=22{\frac{1}{2}}^o$

$\theta ={22}^o{30}^{\prime }$.