If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square
Okay is the diamter of the disk?
We know that,
$\displaystyle \pi r^2=36$
Thus,
$\displaystyle r^2=\frac{36}{\pi}\approx 11.5$
Thus,
$\displaystyle r=\sqrt{11.5}\approx 3.39 \mbox{ cm}$
That means the diamter of the circle is twice as much,
$\displaystyle d\approx 6.77 \mbox{ cm}$
But the diamter of the circle is the hypotenuse of the square.
The square creates a 45,45,90 triangle. Thus, the side of the square is,
$\displaystyle s=\frac{6.77}{\sqrt{2}}\approx 4.79 \mbox{ cm}$
That means the area of the square is,
$\displaystyle A=s^2\approx 22.93 \mbox{ cm}^2$