Question

A point is chosen at random in the square shown below. Find the probability that the point is in the shaded circular region. Each side of the square is 6in, and the radius of the circle is 3in.Use the value 3.14 for π. Round your answer to the nearest hundredth.

Answer 1

We will have the following:

First, we determine the area of the square and of the shaded region, that is:

`\begin{gathered} A_s=6in^2\Rightarrow A_s=36in^2 \\ \\ A_c=\pi(3)^2\Rightarrow A_c=9\pi in^2 \end{gathered}`

Now, we will have that the probability will be of:

`P=(9\pi)/(36)\Rightarrow P=(\pi)/(4)\Rightarrow P\approx0.79`

So, the probability is approximately 79%.