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?

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- Mar 18th 2013, 05:22 PMarb123Help with solving this probability problem
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? - Mar 18th 2013, 06:14 PMchiroRe: Help with solving this probability problem
Hey arb123.

What do you mean for the inner circle? I only see one circle in your diagram and you have the area of that circle in your post. - Mar 18th 2013, 06:18 PMarb123Re: Help with solving this probability problem
I meant the inner square. Sorry!

- Mar 18th 2013, 06:27 PMPazeRe: Help with solving this probability problem
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:

$\displaystyle \frac{\left(r^2\cdot \pi-2\cdot \frac{(2r\cdot r)}{2}\right)}{2r\cdot 2r}$ - Mar 18th 2013, 06:28 PMPazeRe: Help with solving this probability problem
Perhaps chiro can verify my answer?

- Mar 18th 2013, 07:52 PMarb123Re: Help with solving this probability problem
why wouldn't the height also be 2r? when you draw in out the height of each side of the triangle is equal to the base.

- Mar 18th 2013, 08:06 PMPazeRe: Help with solving this probability problem
Does this image help you understand why the height is r and the base is 2r? http://s9.postimage.org/5zb7sblnj/expl.png

- Mar 18th 2013, 08:11 PMarb123Re: Help with solving this probability problem
Yes, i see now! Thank you.