Question

Find that probability that a point chosen at random in the figure lies in the Green circle. The Green Circle has a diameter of 24. (The Green Circle is in the Blue Square)

Answer 1

its like reading bedtime stories to the blind :)

Answer 2

lol

Answer 3

im gonna assume the circle is inscribed in the square ...

the prob will be: area.circle/area.square

Answer 4

The diameter of the circle will be the diagonal of the square.

Answer 5

"side" i think

Answer 6

Oh, bah. I thought the square was inscribed in the circle, not the other way around..

Answer 7

My way was much more interesting.

Answer 8

Also, I don't think you need the diameter.

Answer 9

diam is just for making the area of the square easier to obtain ..

Answer 10

i know how to find the area of the circle but im not sure how to find the area of the square

Answer 11

\[Area_\square = s^2\]\[Area_\bigcirc = \pi r^2 = \pi (\frac{s}{2})^2 = \frac{1}{4}\pi
s^2\]

\[Probability =\frac{Area_\bigcirc}{Area_\square}\]

Answer 12

It's not needed to know the diameter, the s factors cancel.

Answer 13

The area of a square is the length of the side squared.

Answer 14

The length of the side is the diameter of the circle.

Answer 15

So given that the s factors cancel we can tell that it doesn't matter how big the circle is, the probability will always be the same given this arrangement.

Answer 16

i keep getting 21.5% but its not the right answer

Answer 17

Did you do what I wrote above?

Answer 18

\[Probability =\frac{Area_\bigcirc}{Area_\square} = \frac{\frac{1}{4}\pi s^2}{s^2} = \frac{\pi}{4}\]

Answer 19

yea...i think so at least. but im not sure why in order to find the area of a circle you need 1/4?

Answer 20

The area of the circle is \(\pi r^2\). But the r is the diameter divided by 2. The diameter is also the length of one side of the square.

Answer 21

So I wrote my r as being \(\large\frac{s}{2}\)

Answer 22

and when I squared that I got \(\large \frac{s^2}{4}\)

Answer 23

yea i know all of that and this is my equation when i do p r^2 576-452.16/576=123.84/576=0.215 and move the decimal 2 places and get 21.5%

Answer 24

This is why calculators are bad ;p

Answer 25

where is that 576 from?

Answer 26

that's the area of the square?

Answer 27

Oh I see what the problem is.

Answer 28

You have the right value for the areas. You just subtracted them for some reason.

Answer 29

The probability will be the area of the circle divided by the area of the square

Answer 30

no need to subtract

Answer 31

\[\frac{452.16}{576} \approx \frac{\pi}{4} \approx78.54\%\]