Question

A dart hits the circular dartboard at a random point. what is the probability that the dart lands in the shaded square region. the radius of the dartboard 12 inches, and each side of the shaded region is 4 in. use the value 3.14 for pie round to the nearest hundredth

Answer 1

Given: The radius of the circular dart and the length of the shaded region

`\begin{gathered} r_{\text{dartboard}}=12in \\ l_{\text{shaded region}}=4in \end{gathered}`

To Determine: The probability that the dart lands in the shaded square region

The area of the dartboard can be calculated by the formula of a circle

`\begin{gathered} A_{\text{dartboard}}=\pi r^2 \\ \pi=3.14,r=12in \\ A_{\text{dartboard}}=3.14*12^2=3.14*144in^2=452.16in^2 \end{gathered}`

The area of the shaded region can be calculated by the area of a square