Certainly! Let's calculate the volume of an official NBA basketball, given its diameter of 9.5 inches.
### Step-by-Step Solution:
1. Understand the Formula for the Volume of a Sphere:
The formula for the volume [tex]\( V \)[/tex] of a sphere is given by:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
2. Calculate the Radius:
Given the diameter [tex]\( D \)[/tex] of the basketball is 9.5 inches, we can find the radius [tex]\( r \)[/tex] by dividing the diameter by 2:
[tex]\[
r = \frac{D}{2} = \frac{9.5}{2} = 4.75 \text{ inches}
\][/tex]
3. Plug the Radius into the Volume Formula:
Now we substitute [tex]\( r = 4.75 \)[/tex] inches into the volume formula:
[tex]\[
V = \frac{4}{3} \pi (4.75)^3
\][/tex]
4. Calculate [tex]\( (4.75)^3 \)[/tex]:
[tex]\[
4.75^3 = 4.75 \times 4.75 \times 4.75 = 107.171875
\][/tex]
5. Multiply by [tex]\(\frac{4}{3}\)[/tex] and [tex]\(\pi\)[/tex]:
Now, we multiply this result by [tex]\(\frac{4}{3}\)[/tex] and [tex]\(\pi\)[/tex]:
[tex]\[
V = \frac{4}{3} \pi \times 107.171875
\][/tex]
Using [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[
\frac{4}{3} \times 107.171875 \approx 142.8958333 \quad (\text{approximately})
\][/tex]
[tex]\[
V \approx 142.8958333 \times 3.14159 = 449.342 \quad (\text{approximately})
\][/tex]
### Conclusion:
The volume of the basketball is approximately 449.34 cubic inches.
