Question

1. a robot at a carnival booth randomly tosses a dart at a square target with 8 inch sides and a circle with a 3 inch radius in the middle. to the nearest whole percent, what is the probability that the dart will land in the circle?

Explanation:

Step1: Calculate the area of the square

The area formula for a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 8\) inches, so \(A_{square}=8^2=64\) square inches.

Step2: Calculate the area of the circle

The area formula for a circle is \(A=\pi r^2\), where \(r\) is the radius. Given \(r = 3\) inches, so \(A_{circle}=\pi\times3^2 = 9\pi\approx9\times3.14 = 28.26\) square inches.

Step3: Calculate the probability

The probability \(P\) that the dart lands in the circle is \(P=\frac{A_{circle}}{A_{square}}\). Substitute \(A_{circle}=28.26\) and \(A_{square}=64\) into the formula: \(P=\frac{28.26}{64}=0.4415625\).

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by \(100\). So \(P = 0.4415625\times100\%=44.15625\%\).

Answer:

\(44\%\)