To find the volume of a sphere, you can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.
First, we need to find the radius of the basketball. Since the diameter is given as 9 inches, we can find the radius by dividing the diameter by 2:
\[ r = \frac{diameter}{2} = \frac{9 \text{ in}}{2} = 4.5 \text{ in} \]
Now, we can plug the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (4.5)^3 \]
Next, calculate \( (4.5)^3 \):
\[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 20.25 \times 4.5 = 91.125 \]
Now substitute this back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 91.125 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
Now calculate \( V \):
\[ V \approx 4.18667 \times 91.125 \approx 381.5 \text{ in}^3 \]
Therefore, the amount of air needed to fill the basketball is approximately:
\[ \boxed{381.5 \text{ inches cubed}} \]