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

Printable View

- Oct 24th 2006, 02:54 PMRimasgeometry of circle
If the area of a disc insribed in a square is 36 pie cm ^2 what is the area of the square

- Oct 24th 2006, 04:32 PMThePerfectHacker
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,

$\displaystyle A=s^2\approx 22.93 \mbox{ cm}^2$ - Oct 24th 2006, 09:14 PMCaptainBlack