To find the volume of a basketball with a diameter of 9 inches, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius of the sphere. Since the diameter is 9 inches, the radius \( r \) is half of that:
\[ r = \frac{9}{2} = 4.5 , \text{inches} \]
Now we can substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (4.5)^3 \]
First, calculate \( (4.5)^3 \):
\[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 20.25 \times 4.5 = 91.125 \]
Now substitute that back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 91.125 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
Finally, multiply this by \( 91.125 \):
\[ V \approx 4.18667 \times 91.125 \approx 381.5 , \text{in}^3 \]
So, the volume needed to fill the basketball is approximately 381.5 in³.
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