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hichkok12 [17]
2 years ago
6

A circle is inscribed in a square with a side length of 144. If a point in the square is chosen at random, what is the probabili

ty that the point is inside the circle?
Mathematics
1 answer:
____ [38]2 years ago
4 0

Given :

A circle is inscribed in a square with a side length of 144.

So, radius of circle, r = 144/2 = 72 units.

To Find :

The probability that the point is inside the circle.

Solution :

Area of circle,

A_c = \pi r^2\\\\A_c = 3.14 \times 72^2\ units^2\\\\A_c = 16277.76 \ units^2

Area of square,

A_s = (2r)^2\\\\A_s = ( 2 \times 72)^2\ units^2\\\\A_s = 20736\ units^2

Now, probability is given by :

P = \dfrac{A_c}{A_s}\\\\P = \dfrac{16277.76}{20736}\\\\P = 0.785

Therefore, the probability that the point is inside the circle is 0.785 .

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