Question

Find the radius, central angle and perimeter of a sector whose arc length and area are $27.5$ cm and $618.75$ $c{m}^2$ respectively.

Answer 1

Arc length$=27.5cm$

Area of sector$=618.75c{m}^2$

$\Rightarrow \frac{\theta }{360°}\times \pi r^2=618.75c{m}^2$

$\Rightarrow \frac{\theta }{360°}\times 2\pi r=27.5c{m}^2$

$\Rightarrow \frac{\frac{\theta }{360°}\times \pi r^2}{\theta /360°\times 2\pi r}=\frac{618.75}{27.5}\Rightarrow r=\frac{618.75\times 2}{27.5}=45cm$

$\therefore$Radius of sector$=45cm$

$\frac{\theta }{360°}\times 2\times \frac{22}{7}\times 45=27.5\Rightarrow \theta =\frac{27.5\times 360°}{44\times 45}=5°$

Central angle$=5°$

Perrimeter$=\frac{\theta }{360°}\times 2\pi r+2r=27.5++2\times 445=117.5cm$