Final answer:
A regulation NBA basketball has a circumference of about 29.5 inches, and using the formula for the volume of a sphere, we can calculate the volume. None of the provided options (a) 449, (b) 7360, (c) 2900, (d) 1140 cubic inches are correct; the actual volume should be around 455 cubic inches. The correct option is (a) 449
Step-by-step explanation:
The question asks for the volume of a regulation NBA basketball. A regulation NBA basketball has a circumference of about 29.5 inches. To find the volume, we can use the formula for the volume of a sphere, which is V = (4/3)πr^3. Since the diameter is the circumference divided by π (D = C/π), we can find the radius by dividing the diameter by 2. Once we have the radius, we can calculate the volume.
However, the given options (a) 449, (b) 7360, (c) 2900, (d) 1140 cubic inches don’t seem to correspond to the correct volume calculation for a regulation NBA basketball when applying the proper formula. The actual volume should be around 455 cubic inches. Note that a quick mental approximation or an error may lead to one of the provided answers, but with accurate and precise calculations, none of the options provided are correct.
The volume of a regulation NBA basketball can be found using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius of the basketball.
The radius of a regulation NBA basketball is approximately 4.75 inches, so substituting this value into the formula we get:
Volume = (4/3)π(4.75)³ = (4/3)π107.58 ≈ 449.68 cubic inches.
Therefore, the volume of a regulation NBA basketball is approximately 449 cubic inches. The correct option is (a) 449