The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. What is the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim? Show your work. (4 points)
To find the distance between the ball and the rim in a shot where the ball goes exactly in the center of the rim, we first need to calculate the radius of the basketball rim.
The diameter of the rim is 18 inches, so the radius is half of that:
Radius = 18 / 2 = 9 inches
Since the ball goes exactly in the center of the rim, the center of the ball aligns with the center of the rim. Therefore, the distance between the ball and the rim is the difference between the radius of the rim and the radius of the basketball.
The circumference of the basketball is 30 inches, so the diameter of the basketball is:
Diameter = Circumference / π
Diameter = 30 / π
Diameter ≈ 9.55 inches
The radius of the basketball is half of the diameter:
Radius = 9.55 / 2 ≈ 4.78 inches
The distance between the ball and the rim is:
Distance = Radius of the rim - Radius of the basketball
Distance = 9 - 4.78
Distance ≈ 4.22 inches
Therefore, the distance between the ball and the rim in a shot where the ball goes exactly in the center of the rim is approximately 4.22 inches.