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)
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 need to calculate the radius of the rim and the radius of the basketball.
1. Calculate the radius of the rim:
The diameter of the rim is given as 18 inches, so the radius of the rim (r_rim) is half of the diameter:
r_rim = 18 inches / 2 = 9 inches
2. Calculate the radius of the basketball:
The circumference of the basketball is given as 30 inches. We can use the formula for the circumference of a circle to find the radius:
Circumference = 2 * π * radius
30 inches = 2 * π * radius
radius = 30 inches / (2 * π) ≈ 4.77 inches
3. Calculate the distance between the ball and the rim:
The distance between the ball and the rim at the point where the ball goes through the center of the rim is the sum of the radii of the rim and the basketball:
Distance = r_rim + radius
Distance = 9 inches + 4.77 inches
Distance ≈ 13.77 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 13.77 inches.