To find the volume of a basketball (which is a sphere) with a diameter of 9 inches, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to find the radius \( r \) of the basketball. The radius is half the diameter:
\[ r = \frac{diameter}{2} = \frac{9 \text{ in}}{2} = 4.5 \text{ in} \]
Now we can plug the radius into the volume formula. Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (4.5)^3 \]
Calculating \( (4.5)^3 \):
\[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 20.25 \times 4.5 = 91.125 \]
Now substituting back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 91.125 \]
Calculating the multiplication:
\[ 3.14 \times 91.125 \approx 285.1975 \]
Now multiply by \( \frac{4}{3} \):
\[ V = \frac{4 \times 285.1975}{3} \approx \frac{1140.79}{3} \approx 380.2633 \]
Rounding to the nearest tenth:
\[ V \approx 380.3 \text{ in}^3 \]
Now, looking at the options provided:
- 113 in³
- 3,052.1 in³
- 190.8 in³
- 381.5 in³
The closest answer is 4. 381.5 in³.