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,
[tex]A_c = \pi r^2\\\\A_c = 3.14 \times 72^2\ units^2\\\\A_c = 16277.76 \ units^2[/tex]
Area of square,
[tex]A_s = (2r)^2\\\\A_s = ( 2 \times 72)^2\ units^2\\\\A_s = 20736\ units^2[/tex]
Now, probability is given by :
[tex]P = \dfrac{A_c}{A_s}\\\\P = \dfrac{16277.76}{20736}\\\\P = 0.785[/tex]
Therefore, the probability that the point is inside the circle is 0.785 .
