S3-S4 maths probability ques.

[匿名]

2012-07-14 7:15 am

In a 3cmX3cm 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?

(2-DIMENSION)

回答 (1)

fooks

2012-07-14 9:19 am

✔ 最佳答案

Radius of the coin = (1.8 cm)/2 = 0.9 cm
Radius of the dark spot = (1 cm)/2 = 0.5 cm

When the coin is thrown into the box, the distance between the centre of thecoin and the side of the square box ≤ 0.9 cm
Therefore, the centre of the coin must be located at a square,
and the area the square = (3 - 2 x 0.9) cm² = 1.44 cm²

To cover the dark spot, the distance between the centre of coin and the centreof the dark spot ≤ (0.9 - 0.5) cm
Therefore, the centre of the coin must be located at a circle,
and the area of the circle = π(0.9 - 0.5) cm² = 0.16π cm²

The required probability
= 0.16π/1.44
= π/9
≈ 0.349

參考: fooks

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