To find the volume of a sphere, you can 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 from the diameter. The diameter of the basketball is 9.2 inches, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{9.2 \text{ in}}{2} = 4.6 \text{ in} \]
Next, we can substitute the radius into the volume formula, using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]
Calculating \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \text{ in}^3 \]
Now substituting 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 this by \( 97.336 \):
\[ V \approx 4.18667 \times 97.336 \approx 407.51 \text{ in}^3 \]
So the volume of the basketball is approximately 407.51 in³ when rounded to the nearest hundredth.
Thus, the correct response is:
407.51 in.³