Question

the diagram above shows a square with a side of 6. two concentric circles with radii of 1 and 3 have been placed inside the square. assuming a dart randomly strikes the interior region of the square, approximately what is the probability that the dart does not land inside any of the circles?
0.15
0.25
0.20
0.30

Explanation:

Step1: Calculate square area

Area of square: $A_{square} = s^2 = 6^2 = 36$

Step2: Calculate total circle area

Area of circles: $A_{circles} = \pi r_1^2 + \pi r_2^2 = \pi(1^2 + 3^2) = 10\pi \approx 31.42$

Step3: Calculate non-circle area

Non-circle area: $A_{non-circle} = 36 - 31.42 = 4.58$

Step4: Compute target probability

Probability: $P = \frac{4.58}{36} \approx 0.20$

Answer:

0.20