Question

The official size of the spherical basketball used by the National Basketball Association (NBA) is 74.9 cm in circumference. While preparing for a game, a team manager finds a basketball that has a

circumference of only 72.0 cm. Which of the following is closest to the additional volume of air, in cubic centimeters, that must be added to the ball in order to make it the official size? A: 45 cm^3, B: 135cm^3, C: 593cm^3, or D: 790 cm^3 (please help )

Answer 1

The additional volume of air required to inflate a basketball from a circumference of 72.0 cm to the official NBA size of 74.9 cm is approximately 824 cm³, with the closest available answer being D: 790 cm³.

Step-by-step explanation:

To calculate the additional volume of air needed to inflate a basketball from a circumference of 72.0 cm to the official NBA size of 74.9 cm, we can use the formula for the volume of a sphere: V = ⅔πr³. We first need to find the radius for each circumference. The formula relating circumference (C) to radius (r) is C = 2πr.

For the smaller basketball: C = 72.0 cm. Thus, r = C / (2π) = 72.0 cm / (2π) = 11.46 cm (approx.).
For the official size basketball: C = 74.9 cm. Thus, r = C / (2π) = 74.9 cm / (2π) = 11.92 cm (approx.).
Now calculate the volumes:
Vsmall = ⅔π(11.46 cm)³ = 6,299 cm³ (approx.)
Vofficial = ⅔π(11.92 cm)³ = 7,123 cm³ (approx.)
Additional volume required = Vofficial - Vsmall = 7,123 cm³ - 6,299 cm³ = 824 cm³ (approx.).

The closest answer to the additional volume of air needed is D: 790 cm³, even though the exact calculation gives us a slightly higher value.