Question

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find (i) the length of the arc (ii) area of the sector formed by the arc. (Use π = 22/7)

Answer 1

Here, we have θ = 60° and r = 21 cm

(i) The length of the arc is given by
$$\begin{gathered} \frac{60°}{360°}\times 2\mathrm{\pi }\left(21\right) \\ =\frac{1}{6}\times 2\times \frac{22}{7}\times 21 \\ =22\mathrm{cm} \end{gathered}$$


(ii) Area of the sector formed by the arc is given by
$$\begin{gathered} \frac{60°}{360°}\mathrm{\pi }{\left(21\right)}^2 \\ =\frac{1}{6}\times \frac{22}{7}{\left(21\right)}^2 \\ =231{\mathrm{cm}}^2 \end{gathered}$$