Question

A circular wire of radius $3\,cm$ is cut and bent so as to lie along the circumference of a hoop whose radius is $48\,cm$. Find the angle in degrees which is subtended at the centre of hoop.

• A. $21.5^{\circ}$
• B. $23.5^{\circ}$
• C. $22.5^{\circ}$
• D. $24.5^{\circ}$

Answer 1

Answer: (C)

Length of wire $= 2\pi \times 3 = 6\pi \,cm$ and $r = 48\, cm$ is the radius of the hoop. Therefore the angle $\theta$ (in radian) subtended at the centre of the hoop is given by
$\theta=\frac{\text{Arc}} {\text{Radius}}=\frac{6\pi}{48}$
$=\frac{\pi}{8}=22.5^{\circ}$