Question

In a circle of radius 21 cm, an arc subtends an angle of 60^o at the centre. Find (i) the length of the arc, (ii) the area of the sector.

Answer 1

Step 1: Find the length of the arc
$Lengthofthearc=\left(\frac{\theta }{360°}\right)\times 2\mathrm{\pi r}=\left(\frac{{60}^{\circ }}{360°}\right)\times 2\pi \times 21=22\mathrm{cm}$
Step 2: Find the area of the sector.
$Areaofthesector=\left(\frac{\theta }{360°}\right)\times {\mathrm{\pi r}}^2=\left(\frac{{60}^{\circ }}{360°}\right)\times \pi \times {21}^2=231{\mathrm{cm}}^2$