Question

In a circle of radius 21 cm, an arc subtends an angle of ${60}^o$ at the centre. Find the sum of the length of the arc and area of the sector formed by the arc. $[Use\pi =\frac{22}{7}]$

Answer 1

Given radius of circle $=21$ cm

Arc subtends an angle of ${60}^0$ at center.

(i) Length of an arc $=\frac{\theta }{360}\times 2\pi r=\frac{60}{360}\times 2\times \frac{22}{7}\times 21=\frac{1}{6}\times 2\times 22\times 3=22cm$

(ii) Area of sector $=\frac{\theta }{360}\pi r^2=\frac{60}{360}\times \frac{22}{7}(21{)}^2=11\times 3\times 7=231c{m}^2$

$\therefore$ the total sum is $22+231=253$