Question

The radius of a circle is 3.5 cm and area of the sector is 3.85 cm². Find the length of the corresponding arc and the measure of arc.

Answer 1

Given:
Area of the sector = 3.85 cm²
Radius = 3.5 cm
We know:
Area of the sector = $\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{r}^2$

= $\frac{\mathrm{\theta }}{360}\times \frac{22}{7}\times {\left(3.5\right)}^2$

⇒ 3.85 = $\frac{\mathrm{\theta }}{360}\times \frac{22}{7}\times {\left(3.5\right)}^2$

⇒ $\mathrm{\theta }$ = $\frac{3.85\times 7\times 360}{22\times 3.5\times 3.5}$

⇒ $\mathrm{\theta }$ = 36$°$

The measure of the arc is 36$°$.

We have to find the length of the arc (l) of the circle.
Thus, we have:
Length of the arc (l) = $\frac{\theta }{360}\times 2\mathrm{\pi }r$

= $\frac{36}{360}\times 2\times \frac{22}{7}\times 3.5\mathrm{cm}$

= 2.2 cm

Therefore, the length of the arc is 2.2 cm.