Question

The radius of the circle whose arc of length 15 π cm makes an angle of $\frac{3\mathrm{\pi }}{4}$ radian at the centre is
(a) 10 cm
(b) 20 cm
(c) $11\frac{1}{4}\mathrm{cm}$
(d) $22\frac{1}{2}\mathrm{cm}$

Answer 1

(b) 20 cm

$$\begin{gathered} \mathrm{\theta }=\frac{\mathrm{Arc}}{\mathrm{Radius}} \\ \Rightarrow \frac{3\mathrm{\pi }}{4}=\frac{15\mathrm{\pi }}{\mathrm{Radius}} \\ \Rightarrow \mathrm{Radius}=\frac{60}{3}=20\mathrm{cm} \end{gathered}$$