Question

(i) Find the arc length of the sector of radius 14 cm and area 70 $c{m}^2$
(ii) Find the radius of the sector of area 225 $c{m}^2$ and having an arc length of 15 cm
(iii) Find the radius of the sector whose central angle is ${140}^o$ and area 44 $c{m}^2$.

Answer 1

i)$\frac{\theta }{360°}\times \pi r^2=70㎠\Rightarrow \theta =\frac{70\times 360°\times 7}{22\times 14\times 14}=40.91°$

Arc length$=\frac{40.91°}{360°}\times 2\times \frac{22}{7}\times 14=10㎝$

ii)$\frac{\theta }{360°}\times 2\pi r=15㎝=\frac{\theta }{360°}\times \pi r^2=225㎠$

$\frac{\frac{\theta }{360°}\times \pi r^2}{\frac{\theta }{360°}\times 2\pi r}\times \frac{225}{115}\Rightarrow r=15\times 2=30㎝$

iii)$\frac{\theta }{360°}\times \pi r^2=44㎠\Rightarrow \frac{140°}{360°}\times \frac{22}{7}\times r^2=44$

$r^2=\frac{44\times 360°\times 7}{140°\times 22}=36\Rightarrow r=\sqrt{36}=6㎝$