Answer:
radius = 9.4 metros
Explanation:
The area of a circle is all space inside a circle´s circumference.
you know that the area enclosed by a circle of radio r is πr^2 and its central angle is 2π rad or 360°.
Now, from the statement, you know that for a central angle of 2π/11 rad the area of a sector of a circle is 25 m^2.
With this information, you can do a simple rule of three:
[tex]Central Angle (rad) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Area (m^2)\\ \\ 2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \pi r^2\\ \frac{2\pi}{11}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 25\\[/tex]
The previous is a direct proportion, thus, we apply the fundamental rule of proportions doing cross multiply:
[tex]2\pi (25) = \frac{2\pi (\pi r^2)}{11}\\\\(11)50\pi = 2\pi ^{2} r^2 \ \ \ \ \ \ multiply \ both \ sides \ by \ 11\\\\ \frac{550\pi}{2\pi ^{2}} = r^{2} \ \ \ \ \ \ divide \ both \ sides \ by \ 2\pi ^{2} \\\\ r^2 = \frac{275}{\pi } \ \ \ \ \ \ simplify\\\\ r = \sqrt{\frac{275}{\pi }} \ \ \ \ \ \ taking \ the \ square \ root \ both \ sides\\\\ r = 9,3560\\\\ rounding \ to \ one \ decimal \ place:\\ r = 9,4 \ metros[/tex]
Area of the circular sector is the space occupied by the it. The value of the radius of the circle is 9.354 meters.
Area of the circular sector is the space occupied by the it.
The area of the circular sector is the half of the product of angle of the sector and the radius of the circle.
It can be seen as,
[tex]A=\dfrac{1}{2} \times r^2\times\theta[/tex]
Here, [tex]r[/tex] is the radius of the circle and [tex]\theta[/tex] is the angle of the sector.
Given information-
The area of a sector of a circle is 25 m2.
The central angle of the sector is 2π/11 rad.
The radius of the circle has to be find out. Put the values in the above formulas as,
[tex]25=\dfrac{1}{2} \times r^2\times \dfrac{2\pi}{11} \\r^2=\dfrac{25\times11\times2\times7}{2\times22} \\r^2=87.5\\r=9.354\rm m[/tex]
Thus the value of the radius of the circle is 9.354 meters.
Learn more about the area of a circular sector here;
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