Question

An arc of a circle having measure 36° has length 176 m. Find the circumference of the circle.

Answer 1

Given:
Length of the arc, l = 176 m
Corresponding central angle, $\mathrm{\theta }$ = 36$°$
We know:
Length of the arc, l = $\frac{\mathrm{\theta }}{360}\times 2\mathrm{\pi }r$
$\Rightarrow$176 = $\frac{36}{360}\times \mathrm{Circumference}$ (Circumference = 2$\mathrm{\pi }$r)
$\Rightarrow$Circumference = $\frac{176\times 360}{36}$
= 1760 m