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 Mathematics 2

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Sum

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.

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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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Chapter 7: Mensuration - Practice set 7.3 [Page 155]

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Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 7 Mensuration
Practice set 7.3 | Q 11 | Page 155

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