Final answer:
The volume of the basketball with a diameter of 9 inches is calculated using the volume of a sphere formula, V = 4/3πr³. The answer requires computing the cubic volume with the radius being 4.5 inches, resulting in approximately 382π cubic inches. None of the provided choices exactly match the calculated value.
Step-by-step explanation:
To calculate the volume of a basketball with a 9-inch diameter, we must first know the formula for the volume of a sphere:
V = ⅔πr³
Where V is volume, π (pi) is approximately 3.14159, and r is the radius of the sphere. Using the given diameter of 9 inches, we find the radius to be half of that, which is 4.5 inches. We then plug this into our formula:
V = ⅔π(4.5 in)³
⅔× 3.14159 × (4.5 in × 4.5 in × 4.5 in) = 381.70 in³π.
Thus, the choices do not match the calculated value exactly. Careful calculation indicates that the correct answer might be between B and C, on checking the options, the closest is B) 273.4, but when detailed calculations are done, none of the options match exactly. However, if rounded to the nearest tenth, the volume would be approximately 382π, none of the given choices match, so we would need to communicate to the student that there may be an error in the available choices.