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.
The radius of the basketball rim is half of the diameter, so the radius is 18 inches / 2 = 9 inches.
In order for the ball to go through the center of the rim, it must travel a distance equal to the sum of the radius of the rim and the radius of the basketball in all directions. This means the distance between the ball and the rim is equal to the sum of the radii of both the basketball and the rim.
The radius of a basketball is half of the circumference divided by 2π. So, the radius of the basketball is 30 inches / (2 * π) = 30 / 6.28 ≈ 4.77 inches.
Therefore, the distance between the ball and the rim in a shot in which the ball goes exactly in the center of the rim is 9 inches (radius of rim) + 4.77 inches (radius of basketball) = 13.77 inches.