Question

The area of a minor sector of a circle is 3.85 cm² and the measure of its central angle is 36^°. Find the radius of the circle .

Answer 1

Area of minor sector of the circle = 3.85 cm²

Measure of central angle, θ = 36º

Let the radius of the circle be r cm.

Now,

Area of minor sector = 3.85 cm²

$$\begin{gathered} \Rightarrow \frac{\theta }{360°}\times \mathrm{\pi }{r}^2=3.85 \\ \Rightarrow \frac{36°}{360°}\times \frac{22}{7}\times r^2=3.85 \\ \Rightarrow r=\sqrt{\frac{3.85\times 360°\times 7}{36°\times 22}} \\ \Rightarrow r=\sqrt{12.25}=3.5\mathrm{cm} \end{gathered}$$
Thus, the radius of the circle is 3.5 cm.