area bulls eye = pi (6^2)
total area = pi (16)^2
6^2/16^2 = 2^2*3^2 /2^8 = 9/2^6 = 9/64
= .140625
total area = pi (16)^2
6^2/16^2 = 2^2*3^2 /2^8 = 9/2^6 = 9/64
= .140625
The area of a circle can be calculated using the formula: A = πr^2, where A is the area and r is the radius.
Area of the bull's eye:
A_bullseye = π(6^2) = 36π square inches
Area of the entire dartboard:
A_dartboard = π(16^2) = 256π square inches
To find the probability, we divide the area of the bull's eye by the area of the entire dartboard:
P = A_bullseye / A_dartboard = (36π) / (256π) = 36/256 = 9/64 ≈ 0.14
Therefore, the probability that a dart thrown at random within the dartboard will hit the bull's eye is approximately 0.14 or 14%.
The area of the entire dartboard is equal to the area of the circle with radius 16 inches. The formula to calculate the area of a circle is A = π * r^2, where A is the area and r is the radius.
Therefore, the area of the dartboard is A_dartboard = π * (16 inches)^2.
The area of the bull's eye is equal to the area of the circle with radius 6 inches. So, the area of the bull's eye is A_bullseye = π * (6 inches)^2.
To find the probability, we can compare the area of the bull's eye to the area of the dartboard. The probability is given by:
P = A_bullseye / A_dartboard.
Substituting the values we have, we get:
P = (Ï€ * (6 inches)^2) / (Ï€ * (16 inches)^2).
The π (pi) cancels out, so we are left with:
P = (6 inches)^2 / (16 inches)^2.
Simplifying further, we have:
P = 36 / 256.
Thus, the probability that a dart thrown at random within the dartboard will hit the bull's eye is 36/256, or approximately 0.1406, which is equivalent to about 14.1%.