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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 . - Geometry

Question

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

Solution

Area of minor sector of the circle = 3.85 cm2
The measure of a central angle, θ = 36º
Let the radius of the circle be r cm.
Now,
Area of minor sector = 3.85 cm

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

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

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

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

Thus, the radius of the circle is 3.5 cm .

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