Question

A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is 16in, and the radius of the shaded region is 6in.Use the value 3.14 for π. Round your answer to the nearest hundredth.

Answer 1

To find:

The probability that the dart lands in the shaded circular region.

Solution:

It is given that the side of the cardboard is 16 inches and the radius of the circle is 6 inches..

The probability that the dart lands in the shaded circular region is:

$P=\frac{\text{ area of circular region}}{\text{ total area of cardboard}}$

It is known that the area of the circle is:

$A=\pi r^2$

and the area of the square is:

$A=(side)^2$

So, the probability is:

$\begin{gathered} P=\frac{\pi r^2}{(side)^2} \\ =\frac{3.14\times(6)^2}{16^2} \\ =\frac{113.04}{256} \\ =0.441 \end{gathered}$

So, the probability to nearest hundredth is 0.44.