Answer:
So the correct option is First one
i.e [tex]\dfrac{9\pi}{A}=\dfrac{90}{360}[/tex]
Step-by-step explanation:
Given:
Area of Shaded part = 9 π square feet
To Find :
Area of Circle = ?
Solution:
90 degree center angle is equivalent to an area of 9 Π square feet
So, 360 degree center is equivalent to area A which is the area of the complete circle.
So the Ratio will be
[tex]\dfrac{90}{9\pi} =\dfrac{360}{A}[/tex]
Setting the given statements in proportion:
[tex]\dfrac{90}{9\pi} =\dfrac{360}{A}[/tex]
On solving we get the required
[tex]\dfrac{9\pi}{A} =\dfrac{90}{360}[/tex]
So the correct option is First one
i.e [tex]\dfrac{9\pi}{A}=\dfrac{90}{360}[/tex]
Alternate Method:
Shaded part is of 90°
Area of Shaded part = 9 π square feet
And Full Circle is of 360° that is 4 sector of 90°
[tex]\textrm{Area of Circle}=4\times (Shaded\ part)[/tex]
[tex]\textrm{Area of Circle}=4\times 9\pi[/tex]
[tex]\textrm{Area of Circle}=36\pi[/tex]
So the correct option is First one
i.e [tex]\dfrac{9\pi}{A}=\dfrac{90}{360}[/tex]
On solving this we get
[tex]A=36\pi\ feet^{2}[/tex]
