Samuel throws a dart at a circular dartboard. The dartboard has a radius of 16 inches, and the bull's eye in the center of the dartboard has a radius of 6 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull's eye? Round your answer to the nearest tenth.(1 point)
Responses
26.7%
26.7%
37.5%
37.5%
7.1%
7.1%
14.1%
The area of the entire dartboard can be calculated using the formula for the area of a circle: A = πr^2, where r is the radius.
So, the area of the entire dartboard = π(16^2) = 256π square inches.
The area of the bull's eye can be calculated in the same way: A = πr^2, where r = 6.
So, the area of the bull's eye = π(6^2) = 36π square inches.
The probability that a dart thrown at random within the dartboard will hit the bull's eye can be calculated by dividing the area of the bull's eye by the area of the entire dartboard.
Probability = (36π / 256π) * 100% = 14.1%
Therefore, the correct answer is 14.1%.
Round to the nearest tenth, gives 14.1%.
So, the answer is: 14.1%