in a dartboard ther r 2 circles,one large circle n a smaller shaded one inside the larger one. the large circle has a radius of 2 feet n the smaller circle has a diameter of 2 feet. if a dart os thrown at the board wats the probibility that it will land in the shaded region?
To calculate the probability of the dart landing in the shaded region, we need to compare the areas of the shaded region and the entire dartboard.
First, let's find the area of the large circle. The formula to calculate the area of a circle is A = π * r^2, where A represents the area and r represents the radius. In this case, the radius of the large circle is given as 2 feet.
So, the area of the large circle is:
A_large = π * (2 feet)^2
A_large = π * 4 square feet
A_large ≈ 12.57 square feet
To find the area of the shaded region, we need to calculate the area of the smaller circle, which is the shaded region. The diameter is given as 2 feet, and since the radius is half the diameter, the radius of the smaller circle is 1 foot.
Using the same formula as before, the area of the smaller circle is:
A_small = π * (1 foot)^2
A_small = π * 1 square feet
A_small ≈ 3.14 square feet
Now, we can calculate the probability of the dart landing in the shaded region by dividing the area of the shaded region by the area of the entire dartboard (large circle).
P(shaded region) = A_small / A_large
P(shaded region) = 3.14 square feet / 12.57 square feet
P(shaded region) ≈ 0.25 or 25%
Therefore, the probability of the dart landing in the shaded region is approximately 0.25 or 25%.