The volume \( V \) of a sphere can be calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
First, we need to find the radius of the basketball. The diameter is given as 9.2 inches, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]
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 calculate \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \]
Now we can substitute this back into the volume formula:
\[ V \approx \frac{4}{3} \times 3.14 \times 97.336 \]
Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
Now, multiply by \( 97.336 \):
\[ V \approx 4.18667 \times 97.336 \approx 407.51 \text{ in}^3 \]
Thus, rounding to the nearest hundredth, the volume of the basketball is:
\[ \boxed{407.51 \text{ in}^3} \]