# Thread: geometry of circle

1. ## geometry of circle

If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square

2. Originally Posted by Rimas
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,
$\pi r^2=36$
Thus,
$r^2=\frac{36}{\pi}\approx 11.5$
Thus,
$r=\sqrt{11.5}\approx 3.39 \mbox{ cm}$
That means the diamter of the circle is twice as much,
$d\approx 6.77 \mbox{ cm}$
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,
$s=\frac{6.77}{\sqrt{2}}\approx 4.79 \mbox{ cm}$
That means the area of the square is,
$A=s^2\approx 22.93 \mbox{ cm}^2$

3. Originally Posted by Rimas
If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square
See diagram.

Now let r be the radius of the circle then:

36 pi = pi r^2,

and so r=6 cm.

Therefore the side of the square is 12 cm, and its area is
144 sq cm.

RonL