Question

determine the probability that a dart that lands on a random part of the target will land in the shaded scoring section. assume that all squares in the figure and all circles in the figure are congruent unless otherwise marked. round your answer to the nearest tenth of a percent, if necessary. the area of the square is 100 square inches. the area of the

Explanation:

Step1: Calculate area of the whole region

The side - length of the square in the first example is \(s = 10\) inches. The area of the square \(A_{square}=s^{2}=10^{2}=100\) square inches. The radius of the circle \(r=\frac{10}{2}=5\) inches. The area of the circle \(A_{circle}=\pi r^{2}=\pi\times5^{2}=25\pi\approx 25\times 3.14 = 78.5\) square inches.
The probability \(P\) that a dart lands in the shaded (circle) region is given by the ratio of the area of the shaded region to the area of the whole region. So \(P=\frac{A_{circle}}{A_{square}}=\frac{78.5}{100}=0.785\) or \(78.5\%\)

For the second figure:

Step2: Calculate area of the whole region

The radius of the large circle \(R = 18\) inches. The area of the large circle \(A_{total}=\pi R^{2}=\pi\times18^{2}=324\pi\) square inches.

Step3: Calculate area of the non - shaded regions

We need to find the area of the non - shaded parts. However, since the details of the non - shaded parts (the white regions within the circle) are not clearly defined in terms of known geometric shapes' dimensions. Assuming the shaded region is composed of rectangles etc. If we consider the overall method of probability as the ratio of shaded area to total area. But without full information about the non - shaded parts, we assume we are only given the circle and we want to find the probability related to the whole circle area. If we assume the shaded region is the whole circle for simplicity (as no non - shaded details are clear), the probability that a dart lands in the shaded region is \(P = 100\%=1.0\)

For the first part (square and circle problem):

Answer:

\(78.5\%\)