A dartboard consists of a circle inside a rectangle.
the diameter of the circle equals the width of the rectangle. if the length of the rectangle is 20 units and its area is 160 squares units, what is the approximate probability that a dart that lands inside the rectangle will also land inside the circle?
a) .05
b) .25
c) .13
d) .31
y?
area of rectangle = 160
so width = 160/20 = 8
area of circle = π(4^2) = 16π
prob of hitting circle = 16π/160 = .314 , looks like d)
would a partially opened newspaper be a plane and would a woven threads in a piece of cloth be line .
also what would a satellite dish signal be .. line plane or point
To find the approximate probability that a dart that lands inside the rectangle will also land inside the circle, we need to calculate the ratio of the areas of the circle to the rectangle.
From the information given, we know that the length of the rectangle is 20 units and its area is 160 square units. To find the width of the rectangle, we can divide the area by the length:
Width = Area / Length = 160 / 20 = 8 units.
Since the diameter of the circle is equal to the width of the rectangle, the diameter of the circle is also 8 units. This means that the radius of the circle is half of the diameter, which is 8 / 2 = 4 units.
To find the area of the circle, we can use the formula A = πr², where A is the area and r is the radius:
Area of the circle = π * (4^2) = π * 16 ≈ 50.27 square units.
Now we can calculate the probability by dividing the area of the circle by the area of the rectangle:
Probability = Area of Circle / Area of Rectangle ≈ 50.27 / 160 = 0.314 = 31.4%
So, the approximate probability that a dart that lands inside the rectangle will also land inside the circle is approximately 31.4%.
Looking at the answer choices, the closest option is d) 0.31, which represents 31%.