Question

the diagram above shows a square with a side of 6. three concentric circles with radii of 1, 2 and 3 have been placed inside the square. assuming a dart randomly strikes the interior region of the square, what is the probability that the dart lands inside the donut area between the circle a with radius of 2 and the circle with a radius of 3?
\\(\frac{5}{16}\pi\\)
\\(\frac{1}{9}\pi\\)
\\(\frac{5}{36}\pi\\)
\\(\frac{5}{9}\pi\\)

Explanation:

Step1: Calculate donut area

$\text{Area} = \pi(3^2 - 2^2) = 5\pi$

Step2: Calculate square area

$\text{Area} = 6 \times 6 = 36$

Step3: Compute probability

$\text{Probability} = \frac{5\pi}{36}$

Answer:

$\frac{5}{36}\pi$