#### Question

The area of a minor sector of a circle is 3.85 cm^{2 }and the measure of its central angle is 36^{°}. Find the radius of the circle .

#### Solution

Area of minor sector of the circle = 3.85 cm^{2}

Measure of central angle, *θ* = 36º

Let the radius of the circle be *r* cm.

Now,

Area of minor sector = 3.85 cm^{2 }

\[\Rightarrow \frac{\theta}{360° } \times \pi r^2 = 3 . 85\]

\[ \Rightarrow \frac{36° }{360 ° } \times \frac{22}{7} \times r^2 = 3 . 85\]

\[ \Rightarrow r = \sqrt{\frac{3 . 85 \times 360° \times 7}{36° \times 22}}\]

\[ \Rightarrow r = \sqrt{12 . 25} = 3 . 5 cm\]

Thus, the radius of the circle is 3.5 cm .

Is there an error in this question or solution?

Solution 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 . Concept: Perimeter and Area of a Circle.