To find the volume of a sphere, we 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 determine the radius of the basketball. The diameter 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:
\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]
Calculating \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \]
Now we can find the volume:
\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
Now calculate the volume:
\[ V \approx 4.18667 \times 97.336 \approx 407.47 \text{ in}^3 \]
Rounding to the nearest hundredth, we get:
\[ V \approx 407.47 \text{ in}^3 \]
Among the options provided, the closest value is:
3. 407.51 in.³.
This seems to be a typo since 407.47 is rounded properly to 407.50. Therefore the answer is indeed 407.51 in.³.