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The area of a sector of a circle is represented by A=5/18πr to the power of 2, where r is the radius of the circle (in meters). What is the radius when the area is 40π square meters?
[tex] 40\pi = \frac{5}{18} \pi {r}^{2} [/tex]
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The area of a sector of a circle is represented by A518πr to the power of 2 where r is the radius of the circle in meters What is the radius when the area is 40 class=

Respuesta :

Answer:

r = 12

Step-by-step explanation:

given

A = [tex]\frac{5}{18}[/tex] πr² and A = 40π

Equate the 2 areas and solve for r, that is

[tex]\frac{5}{18}[/tex] πr² = 40π

Multiply both sides by 18 to eliminate the fraction

5πr² = 720π ( divide both sides by 5π )

r² = [tex]\frac{720\pi }{5\pi }[/tex] = 144

Take the square root of both sides

r = [tex]\sqrt{144}[/tex] = 12

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