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. The radius is half of the diameter. Thus:
\[ r = \frac{9}{2} = 4.5 , \text{inches} \]
Now, substituting \( r \) into the volume formula:
\[ V = \frac{4}{3} \pi (4.5)^3 \]
Calculating \( (4.5)^3 \):
\[ (4.5)^3 = 4.5 \times 4.5 \times 4.5 = 91.125 \]
Now substitute \( \pi \) with 3.14:
\[ V = \frac{4}{3} \times 3.14 \times 91.125 \]
Calculating the volume step-by-step:
-
Calculate \( \frac{4}{3} \times 3.14 \): \[ \frac{4}{3} \times 3.14 \approx 4.1867 \]
-
Now multiply by \( 91.125 \): \[ V \approx 4.1867 \times 91.125 \approx 381.5 , \text{in}^3 \]
Therefore, the volume of the basketball is approximately 381.5 inches cubed.
The correct answer is:
381.5 in.³