Question

A circle is inscribed in a square. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

Answer 1

`a-side\ length\ of\ the\ square\\r=(1)/(2)a-radius\ length\ of\ the\ circle\\\\A_{\fbox{}}=a^2\\\\A_O=\pi r^2=\pi\left((1)/(2)a\right)^2=(1)/(4)\pi a^2\\\\Probability:((1)/(4)\pi a^2)/(a^2)=(1)/(4)\pi\approx(1)/(4)\cdot3.14=0.785`