The object of the game is to toss a beanbag in the circular hole of a 48-by-24 inch board. If the diameter of the circle is 6 inches, what is the geometric probability an object will hit the circle on the board? Assume that the object will hit the board. Show your work or explain how you got your answer.
Formulas Needed:
Area of a rectangle: Area = Length x Width
Area of a circle: Area = π x radius^2
Radius = 1/2(diameter)
To find the geometric probability, we need to find the ratio of the area of the circle to the area of the entire board.
The diameter of the circle is given as 6 inches, so the radius is 1/2 × 6 = 3 inches.
The area of the circle is given by the formula: Area = π × radius^2.
Plugging in the values, we get: Area = π × 3^2 = 9π square inches.
The area of the board is given as 48 × 24 = 1152 square inches.
So the ratio of the area of the circle to the area of the board is: (9π) / 1152.
The geometric probability is the ratio of the desired outcome (hitting the circle) to the total possible outcomes (hitting anywhere on the board). Therefore, the geometric probability of hitting the circle on the board is: (9π) / 1152.