In a circle of radius 21 cm,

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)

Solution:

Here, we have θ = 60° and r = 21 cm

(i) The length of the arc is given by

$\frac{60^{\circ}}{360^{\circ}} \times 2 \pi(21)$

$=\frac{1}{6} \times 2 \times \frac{22}{7} \times 21$

$=22 \mathrm{~cm}$

(ii) Area of the sector formed by the arc is given by

$\frac{60^{\circ}}{360^{-}} \pi(21)^{2}$

$=\frac{1}{6} \times \frac{22}{7}(21)^{2}$

$=231 \mathrm{~cm}^{2}$