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, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.
First, we need to find the radius of the basketball. The diameter is given as 9.2 inches, so the radius is half of the diameter:
\[ r = \frac{diameter}{2} = \frac{9.2}{2} = 4.6 , \text{inches} \]
Next, we can plug the radius into the volume formula:
\[ V = \frac{4}{3} \pi r^3 \]
Substituting in the values:
\[ V = \frac{4}{3} \times 3.14 \times (4.6)^3 \]
Calculating \( (4.6)^3 \):
\[ (4.6)^3 = 4.6 \times 4.6 \times 4.6 = 97.336 \]
Now substituting back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 97.336 \]
Calculating the multiplication:
- First calculate \( 3.14 \times 97.336 \):
\[ 3.14 \times 97.336 \approx 305.43384 \]
- Now multiply by \( \frac{4}{3} \):
\[ V = \frac{4}{3} \times 305.43384 \approx 407.24512 \]
Now, rounding to the nearest hundredth:
\[ V \approx 407.25 , \text{cubic inches} \]
Thus, the volume of the basketball is approximately 407.25 cubic inches.