Question

Please help! :)

Answer 1

Answer:

So the correct option is First one

i.e $\dfrac{9\pi}{A}=\dfrac{90}{360}$

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

$\dfrac{90}{9\pi} =\dfrac{360}{A}$

Setting the given statements in proportion:

$\dfrac{90}{9\pi} =\dfrac{360}{A}$

On solving we get the required

$\dfrac{9\pi}{A} =\dfrac{90}{360}$

So the correct option is First one

i.e $\dfrac{9\pi}{A}=\dfrac{90}{360}$

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°

$\textrm{Area of Circle}=4\times (Shaded\ part)$

$\textrm{Area of Circle}=4\times 9\pi$

$\textrm{Area of Circle}=36\pi$

So the correct option is First one

i.e $\dfrac{9\pi}{A}=\dfrac{90}{360}$

On solving this we get

$A=36\pi\ feet^{2}$