Question

(i) Find the angle subtended by an arc $88$ cm long at the center of a circle of radius $42$ cm.
(ii) The arc length of a sector of a circle of radius $14$ cm is $22$ cm. Find its central angle.
(iii) Find the radius of a sector of a circle having a central angle ${70}^o$ and an arc length of $44$ cm.

Answer 1

i)Arc length$=88cm=\frac{\theta }{360°}\times 2\pi r=88cm$

$\Rightarrow \frac{\theta }{360°}\times 2\times \frac{22}{7}\times 42=88\Rightarrow \theta =\frac{88\times 7\times 360°}{44\times 42}=120°$

ii)$\frac{\theta }{360°}\times 2\pi r=22cm\Rightarrow \theta =\frac{22\times 7\times 360°}{44\times 14}=90°$

iii)$\frac{\theta }{360°}\times 2\pi r=44cm\Rightarrow r=\frac{44\times 360°\times 7}{44\times 70°}=36cm$