To find the probability that a point placed randomly in the figure (the square) will be inside the circle, we need to calculate the areas of both the circle and the square.
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Area of the circle: The formula for the area \(A\) of a circle is given by:
\[ A = \pi r^2 \]
where \(r\) is the radius. Here, the radius \(r = 4\) cm.
\[ A_{\text{circle}} = \pi (4^2) = \pi \times 16 = 16\pi \]
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Area of the square: The formula for the area \(A\) of a square is given by:
\[ A = s^2 \]
where \(s\) is the side length. Here, the side length \(s = 8\) cm.
\[ A_{\text{square}} = 8^2 = 64 \]
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Probability of selecting a point inside the circle: The probability \(P\) is given by the ratio of the area of the circle to the area of the square.
\[ P = \frac{A_{\text{circle}}}{A_{\text{square}}} = \frac{16\pi}{64} = \frac{\pi}{4} \]
Using the approximate value of \(\pi \approx 3.14\):
\[ P \approx \frac{3.14}{4} \approx 0.785 \]
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Rounding to the nearest hundredth: We round \(0.785\) to:
\[ 0.79 \]
Thus, the probability that a randomly placed point in the square will be inside the circle is:
\[ \boxed{0.79} \]