Question

The central angles of two sectors of circles of radii $7cm$ and $21cm$ are respectively ${120}^o$ and ${40}^o$. Find the area of the two sectors as well as the lengths of the corresponding arcs. what do you observe?

Answer 1

Radius of first circle $7cm$

Angle at center ${120}^{\circ }$

Length of arc is given by $\frac{120}{360}\times 2\pi \times 7\frac{1}{3}\times 2\times \frac{22}{7}\times 7\frac{44}{3}$

Radius of Second circle $21cm$

Angle at center ${40}^{\circ }$

Length of arc is given by $\frac{40}{360}\times 2\pi \times 21\frac{1}{9}\times 2\times \frac{22}{7}\times 21\frac{44}{3}$

In both the cases the length of arcs are same To keep the length of arc to be constant the radius and angle at center must be inversly proportional.