To solve the problem, we first need to find the areas of both the square and the circle.
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Area of the square: The area \( A_{\text{square}} \) of a square is given by the formula: \[ A_{\text{square}} = \text{side}^2 \] Here, the side length of the square is 8 cm, so: \[ A_{\text{square}} = 8^2 = 64 \text{ cm}^2 \]
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Area of the circle: The area \( A_{\text{circle}} \) of a circle is given by the formula: \[ A_{\text{circle}} = \pi r^2 \] Here, the radius \( r \) of the circle is 4 cm, so: \[ A_{\text{circle}} = \pi (4^2) = \pi \cdot 16 = 16\pi \text{ cm}^2 \]
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Area not inside the circle: The area outside the circle but inside the square is given by: \[ A_{\text{outside}} = A_{\text{square}} - A_{\text{circle}} = 64 - 16\pi \]
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Probability that a point placed randomly is not inside the circle: The probability \( P \) that a point chosen randomly from the square is outside the circle is: \[ P = \frac{A_{\text{outside}}}{A_{\text{square}}} = \frac{64 - 16\pi}{64} \]
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Calculating the probability: We will compute this probability and round it to the nearest hundredth. Using \( \pi \approx 3.14 \), we can calculate: \[ A_{\text{circle}} \approx 16 \cdot 3.14 = 50.24 \] \[ A_{\text{outside}} \approx 64 - 50.24 = 13.76 \] \[ P \approx \frac{13.76}{64} \approx 0.215 \]
Now, rounding to the nearest hundredth: \[ P \approx 0.22 \]
Thus, the probability that a point placed randomly in the figure is not inside the circle is \( \boxed{0.22} \).