Question

a dart hits the circular dartboard at a random point. find the probability that dart lands in the shaded square region. radius of the dartboard: 12 ineach side of the shaded region: 4 inuse the value 3.14 for pie round to the nearest hundredth

Answer 1

Given:

Radius of the dartboard is 12in.

Each side of the shaded region is 4in.

$\begin{gathered} \text{Total area of the circle=}\pi(r^2) \\ =3.14\times12\times12 \\ =452.16in^2 \end{gathered}$$\begin{gathered} \text{Area of the shaded region=4}\times4 \\ =16in^2 \end{gathered}$$\begin{gathered} Probability\text{ that dart lands in the shaded region=}\frac{16}{452.16} \\ =0.04 \end{gathered}$