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

We know, minor sector area =$\bf{\frac{\pi r^2}{360^{\circ}}\theta}$
Here, r is the radius of circle and θ is the central angle

Given, θ = 36° and area of minor sector = 3.85 cm
∴ area of minor sector = π r²/360° × 36°
3.85 = 22/7 × r²/10
38.5 × 7 = 22r²
3.5 × 3.5 = r²
Taking square root both sides,
r = 3.5 cm

Hence, radius of the cricle is 3.5 cm