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.

Diameter of the basketball rim = 18 inches

Circumference of the standard basketball = 30 inches

Area of circle = π r²  

Basketball rim = 3.14 * (18/2)² = 3.14 * 9² = 3.14 * 81 = 254.34 in²

Circumference of a circle = 2 π r

30 = 2 * 3.14 * r

r = 30 / (2*3.14) = 30 / 6.28 = 4.78 inches

Standard basketball = 3.14 * (4.78)² = 3.14 * 22.85 = 71.75 in²

254.34 - 71.75 = 182.59 in²

x = 3 ± √(5+y)