Question

the diagram above shows a square with a side of 6 and a circle with radius of 2 drawn on a coordinate system. assuming a dart randomly strikes the interior region of the square, approximately what is the probability that the dart does not land inside the circle?
0.62
0.65
0.60
0.68

Explanation:

Step1: Calculate square area

Area of square: $A_s = s^2 = 6^2 = 36$

Step2: Calculate circle area

Area of circle: $A_c = \pi r^2 = \pi (2)^2 = 4\pi \approx 12.57$

Step3: Find non-circle area

Area of square minus circle: $A_s - A_c \approx 36 - 12.57 = 23.43$

Step4: Compute target probability

Probability = $\frac{\text{Non-circle area}}{\text{Square area}} \approx \frac{23.43}{36} \approx 0.65$
Correction note: Using $\pi \approx 3.1416$, $4\pi=12.5664$, $36-12.5664=23.4336$, $\frac{23.4336}{36}=0.6509$, which rounds to 0.65. However, if using $\pi \approx 3.14$, $4\pi=12.56$, $36-12.56=23.44$, $\frac{23.44}{36}\approx0.651$, still ~0.65. The closest option is 0.65.

Revised Final Answer:

0.65

Revised Explanation:

Step1: Compute square area

$A_s = 6^2 = 36$

Step2: Compute circle area

$A_c = \pi(2)^2 = 4\pi \approx 12.57$

Step3: Calculate non-circle area

$36 - 12.57 = 23.43$

Step4: Find desired probability

$\frac{23.43}{36} \approx 0.65$

Answer:

0.60