To find the volume of a basketball using the formula for 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 determine the radius of the basketball. Since the diameter is 9.2 inches, the radius is:
\[ r = \frac{\text{diameter}}{2} = \frac{9.2}{2} = 4.6 \text{ inches} \]
Next, we can plug the radius into the volume formula. Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]
Calculating \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \]
Now, substitute this back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]
Now, calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
Now multiply by \( 97.336 \):
\[ V \approx 4.18667 \times 97.336 \approx 407.51 \]
Thus, the volume of the basketball is approximately \( 407.51 \) cubic inches.
Finally, rounding to the nearest hundredth, the volume is:
\[ \text{Volume} \approx 407.51 \text{ in}^3 \]
So the correct answer is:
407.51 in.³
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