All I'm worried about it is (a); for now. Okay, so let's start off like this: I know what the question is asking, sort of. I know it wants the ratio of the inside corner pieces of the square to the square itself. But what??? I obviously know that $A_{circle}=\pi r^2$ and $A_{square}=wh$ and also that the piece they are looking for is $A_{circle}-A_{square}$ but the ratio? I don't understand that. Can someone explain to me what they mean by that and stay posted for I may have questions about (b)-(e). Thanks.
[Math] Find the ratio of the area inside the square but outside the circle to the area of the square in the figure.
algebra-precalculusgeometry
Related Solutions
Hint: Think about the relationship between the radius of the circle, the diameter of the circle, and the side length of the square.
$\hskip1.5in$ 
Do you know the area of a square given its side length?
The circle of radius R in the square of side C is such :
$ 2 R = C$
Area of the circle $\pi R^2$ , of the square $C^2$ , and the ratio of circle on square is :
and the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{4 R^2} = \frac{\pi}{4} $
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{4} 100 cm^2 \approx 78.54 cm^2$
The square of side C in the circle of radius R is such :
$C^2 = R^2 + R^2$
similarly the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{2 R^2} = \frac{\pi}{2} $
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{2} 100 cm^2 \approx 157,08 cm^2$
Best Answer
If $A_0$ is the total area of the four corner pieces, and $A_1$ is the area of the square, they want $\frac{A_0}{A_1}$: that fraction is by definition the ratio of $A_0$ to $A_1$. Note also that for the square you have $w=h=2r$.