I know that you have to do
area of circle-area of inner square
Area of outer square
the area of the circle= (3.1413)r^2
the area of outer square= 4r^2
But i cant figure out the area of the inner circle?
can anyone help me?
I know that you have to do
area of circle-area of inner square
Area of outer square
the area of the circle= (3.1413)r^2
the area of outer square= 4r^2
But i cant figure out the area of the inner circle?
can anyone help me?
Hi arb123.
Notice that if you split the inner square into two triangles, you will have two triangles with base 2r and height r.
We have:
A circle with area: $\displaystyle r^2\cdot \pi$
A square with area: $\displaystyle 2\cdot \frac{(2r\cdot r)}{2}$
A larger square with area: $\displaystyle 2r \cdot 2r$
The shaded area is thus: $\displaystyle \left(r^2\cdot \pi-2\cdot \frac{(2r\cdot r)}{2}\right)$
The probability of the dart hitting the shaded area and NOT the white area inside the larger square, between its corners and the circle is thus:
$\displaystyle \frac{\left(r^2\cdot \pi-2\cdot \frac{(2r\cdot r)}{2}\right)}{2r\cdot 2r}$
Does this image help you understand why the height is r and the base is 2r? http://s9.postimage.org/5zb7sblnj/expl.png