Question

I am going to attach a picture of the question now I have to type out how she got the answer for this question I need the answer fast bc this is due in an hour.

Answer 1

First we find the area of the whole circle by the formula

$A=\pi\times r^2$

where r is the radious

replacing

$\begin{gathered} A=\pi\times9^2 \\ A=81\pi \end{gathered}$

whole area or the area corresponding to 360° is 81pi

Then the angle of the shaded area is the total less 90° because the square on the vertex of the angle represents 90°

$360-90=270$

andgle of the shaded area is 270°

now we can make a relation, if the area of 360 is 81pi whats the area of 270°

$\begin{gathered} 360\longrightarrow81\pi \\ 270\longrightarrow x \end{gathered}$

where x is the area for 270° of the circle

we solve using cross multiplication

the value of x is the multiplication of the diagonla numbers(270 and 81pi) between 360

$\begin{gathered} x=\frac{270\times81\pi}{360} \\ \\ x=\frac{243}{4}\pi\approx190.85 \end{gathered}$

the area of the shaded region is 190.85 or 191 square meters, then right option is D