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A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is
15in
, and the radius of the shaded region is
5in
.
Use the value
3.14
for
π
. Round your answer to the nearest hundredth.
https://www.jiskha.com/display.cgi?id=1502332483
To find the probability that the dart lands in the shaded circular region, we need to find the area of the shaded region and divide it by the total area of the dartboard.
First, let's find the area of the shaded region. The shaded region is a circle, and the formula for the area of a circle is given by:
A = πr^2
Where A is the area and r is the radius of the circle.
In this case, the radius of the shaded region is given as 5 inches. So, substituting the values into the formula, we have:
A = 3.14 * (5)^2 = 3.14 * 25 = 78.5 square inches
Next, let's find the total area of the dartboard. The dartboard is a square, and the formula for the area of a square is given by:
A = s^2
Where A is the area and s is the length of one side of the square.
In this case, each side of the dartboard is given as 15 inches. So, substituting the value into the formula, we have:
A = (15)^2 = 225 square inches
Now, we can calculate the probability by dividing the area of the shaded region by the total area of the dartboard:
P(shaded region) = Area of shaded region / Total area of dartboard
P(shaded region) = 78.5 square inches / 225 square inches
P(shaded region) ≈ 0.35
Therefore, the probability that the dart lands in the shaded circular region is approximately 0.35, rounded to the nearest hundredth.