Pi?

The formula for the area of the circle is: $\pi r^2$ .

The side of the square is $2$ times the radius of the circle, therefore the result is:

$\dfrac{\pi r^2}{(2r)^2}$ $\Rightarrow \dfrac{\pi r^2}{4r^2}=\boxed{\dfrac{\pi}{4}}$

Area of circle $\frac { \Pi \quad { \left( diameter \right) }^{ 2 } }{ 4 }$

Area of square ${ \left( side\right) }^{ 2 }$

Ratio between areas of circle and square = $\frac { \frac { \Pi \quad { \left( d \right) }^{ 2 } }{ 4 } }{ { \left( d \right) }^{ 2 } }$

And the answer is $\frac { \Pi }{ 4 }$

The ratio of the area of a circle, $\pi r^2$ , to the area of a square of side length $r$ , $r^2$ is $\pi$ . The side of the big square is $(2r)^2$ . This is four times bigger than $r^2$ , so the ratio is reduced by a factor of $4$ and becomes $\frac{\pi}{4}$ .

$\displaystyle \left ( 2r \right ) ^ { 2 } : \pi r ^ { 2 } \rightarrow 4r ^ { 2 } : \pi r ^ { 2 } \Rightarrow 4 : \pi$

$\displaystyle \therefore \frac { \pi } { 4 }$

Area of the circle: π r2 . Area of the square: (2r)2 . Ratio: π r2 / (2r)2 : π r2 / 4 r2 : π / 4

You can use this to estimate Pi by simulating throwing darts at a dart board...

that's simple buddy.... have a fun.. :-)

Let a is the side of square.... So the radius of circle is a/2 ..... Area of circle = Pi * (a/2)^2 Area of square = a^2 Ratio of circle to square is =( pi (a^2 / 4) ) / a^2 = pi/4 ...

Let $r$ =Radius.The length of the square is $2r$ .So area of square is $l^2=(2r)^2=4r^2$ .Area of circle is $\pi r^2$ .So $Area\;of\;circle:Area\;of\;square=\pi r^2:4r^2=\pi:4=\boxed{\frac{\pi}{4}}$

metal solving = pi/4

Let the side of the square = 2 r

Then

The area of the square = 4 r^2

The area of the circle = Pi r^2

Then

The ratio = Pi/4