To calculate the volume of a sphere, we 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 of the basketball. The diameter is given as 9 inches, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{9 \text{ in}}{2} = 4.5 \text{ in} \]
Next, we substitute the radius into the volume formula using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \cdot 3.14 \cdot (4.5)^3 \]
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 equation:
\[ V = \frac{4}{3} \cdot 3.14 \cdot 91.125 \]
Calculating \( \frac{4}{3} \cdot 3.14 \):
\[ \frac{4}{3} \cdot 3.14 \approx 4.18667 \]
So now calculate:
\[ V \approx 4.18667 \cdot 91.125 \approx 381.76 \]
Rounding this to the nearest tenth gives:
\[ V \approx 381.8 \text{ in}^3 \]
Therefore, the amount of air needed to fill the basketball is approximately 381.5 inches cubed.
So the correct response is:
381.5 in.³
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