To find the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
First, we need to find the radius of the basketball. The diameter of the basketball is given as 9.2 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{d}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]
Now we can substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]
First, we need to calculate \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \]
Now we substitute that back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
Now multiplying by \( 97.336 \):
\[ V \approx 4.18667 \times 97.336 \approx 407.51 \]
Rounding to the nearest hundredth, the volume of the basketball is approximately:
\[ \boxed{407.51 \text{ in}^3} \]
Thus, the correct response is: 407.51 in.³.