Garrett throws a dart at a circular dart board. The dart board has a radius of 18 inches, and the bull’s eye in the center of the dart board has a radius of 4 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, if necessary.
To find the probability that a dart thrown at random within the dartboard will hit the bull's eye, we need to compare the area of the bull's eye to the total area of the dart board.
The total area of the dart board is given by the formula for the area of a circle: A = πr^2, where r is the radius of the dart board. Plugging in r = 18 inches, we get:
A = π*(18)^2 = 324π square inches
The area of the bull's eye is also given by the formula for the area of a circle: A = πr^2, where r is the radius of the bull's eye. Plugging in r = 4 inches, we get:
A = π*(4)^2 = 16π square inches
Therefore, the probability that a dart thrown at random within the dartboard will hit the bull's eye is:
P = (area of bull's eye) / (total area of dart board)
P = 16π / 324π
P = 16 / 324
P ≈ 0.0494
Rounded to the nearest tenth, the probability is approximately 0.1.