If you are throwing a dart at the circular target pictured below, and it is equally likely to hit any point on the target, what is the probability that the dart will hit any of the small inner circles?
Use 3.14 for , and round your answer to the nearest tenth.
A. 6.3%
B. 23.8%
C. 31.3%
D. 35.5%
Please post your answers to your previous questions before you post any more questions.
To find the probability that the dart will hit any of the small inner circles, we need to calculate the ratio of the area of the small inner circles to the area of the entire target.
Let's assume that the radius of the small inner circle is r. The radius of the big circle is twice the radius of the small inner circle, so it is 2r.
The area of a circle is given by the formula A = πr^2. Therefore, the area of the small inner circle is πr^2 and the area of the big circle is π(2r)^2 = 4πr^2.
To calculate the probability, we divide the area of the small inner circles by the area of the big circle and multiply by 100 to express it as a percentage:
Probability = [(πr^2) / (4πr^2)] * 100
The π's cancel out in the numerator and denominator, leaving us with:
Probability = [(r^2) / (4r^2)] * 100
The r^2 cancels out, giving us:
Probability = (1/4) * 100 = 25%
Note that we don't need to use the approximation 3.14 for π in this case because the π's cancel out in the equation.
Rounding the answer to the nearest tenth, the probability that the dart will hit any of the small inner circles is 25%.
Therefore, the correct answer is not listed among the options provided.