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 can create a right triangle using the radius of the rim, the radius of the ball, and the distance we're looking for.
First, we need to find the radius of the basketball rim. The diameter is given as 18 inches, so the radius is half of that: 18/2 = 9 inches.
Next, we find the radius of the basketball. The circumference of a circle is calculated as 2 * π * r, where r is the radius. In this case, the circumference is given as 30 inches, so we can solve for the radius:
30 = 2 * π * r
r = 30 / (2 * π)
r ≈ 4.77 inches
Now we have the two radii, so we can create a right triangle with the distance we're looking for as the hypotenuse. The difference between the two radii is the adjacent side and the distance we're looking for is the opposite side. Using the Pythagorean theorem, we can solve for the distance:
(distance)^2 = (9 - 4.77)^2 + 9^2
(distance)^2 = 21.56 + 81
(distance)^2 = 102.56
distance ≈ √102.56
distance ≈ 10.13 inches
Therefore, the distance between the center of the basketball and the center of the rim in this shot is approximately 10.13 inches.