F.3 probability~.....

用戶36732

2009-07-26 8:25 am

In a 3cm x 3cm square card box, there is a circular dark spot of diameter 1cm located at the centre of the box. Katharine throws a coin of diameter 1.8cm into the box. How likely will the coin fully cover the dark spot?

回答 (1)

六呎將軍

2009-07-26 9:19 am

✔ 最佳答案

With reference to the diagram below:

圖片參考：http://i388.photobucket.com/albums/oo325/loyitak1990/Jul09/Crazyprob1.jpg

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Thus, the possible area is a 1.2 cm by 1.2 cm square = 1.44 cm2.
Then, for the acceptable area, it should be a circle so that the longest possible from its circumference to any point on the dark spot is 0.9 cm which is the radius of the coin.
Suppose that the radius of the acceptable area is r, then from the diagram:
0.9 + (0.5 - r) = 1
r = 0.4 cm
So acceptable area = 0.42 x π
Finally, the probability is 0.42 x π/1.44 = 0.349

參考: Myself

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