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,
- \( r \) is the radius of the sphere.
First, we need to find the radius. The diameter of the basketball is given as 9.2 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{9.2}{2} = 4.6 \text{ inches} \]
Now, we can substitute the radius into the volume formula:
\[ V = \frac{4}{3} \pi (4.6)^3 \]
Calculating \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \]
Now substituting this 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 multiply this by \( 97.336 \):
\[ V \approx 4.18667 \times 97.336 \approx 407.506 \]
Rounding to the nearest hundredth gives:
\[ V \approx 407.51 \]
Thus, the volume of the basketball is approximately:
\[ \boxed{407.51 \text{ in}^3} \]
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