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The area of a sector is $ 120\pi $ and the arc measure is $ {160^o} $ . What is the radius of the circle?
A. $ 16.43 $
B. $ 11.43 $
C. $ 12.23 $
D. $ 10.43 $

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Last updated date: 20th Jul 2024
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Answer
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Hint: Sector of circle: A sector of circle is also known as the disk sector that is formed by two radii and an arc of circle. Where the smaller area is called the minor sector and the biggest area is called the major sector.
As we know that area of sector
 $ Are{a_{\sec tor}} = \dfrac{n}{{360}}\pi {r^2} $
Here
n=angle
r=radius
We can simply put value in the given equation and calculate the value of n from it.

Complete step by step solution:
Given,
Angle, $ n = 160 $
Area of sector, $ {A_s} = 120\pi $
Radius, $ R = ? $
As we know that
 $ Are{a_{\sec tor}} = \dfrac{n}{{360}}\pi {r^2} $
Put the value
 $ \Rightarrow 120\pi = \dfrac{{160}}{{360}}\pi {r^2} $
 $ \pi = \dfrac{{22}}{7} $
 $ \Rightarrow 120\pi = \dfrac{{160}}{{360}}\pi {r^2} $
Simplify the equation
 $ \Rightarrow {r^2} = \dfrac{{120 \times 360}}{{160}} $
 $ \Rightarrow {r^2} = \dfrac{{43200}}{{160}} $
 $ \Rightarrow {r^2} = 270 $
 $ \Rightarrow r = \sqrt {270} $
 $ \Rightarrow r = 16.43 $
Hence the answer is (A) $ 16.43 $.

Note: A circular segment is a region of a circle which is cut-off from the rest of the circle by a secant or a chord. A circular segment is a region of two-dimensional space that is bounded by an arc of a circle and by the cord connecting the endpoints of the arc.