To find the volume of a baseball given its diameter, we can use the formula for the volume of a sphere. Let's go through this step-by-step:
1. Identify the Given Information:
- The diameter of the baseball is 3 inches.
2. Calculate the Radius:
- The radius [tex]\( r \)[/tex] is half of the diameter.
- [tex]\( r = \frac{\text{diameter}}{2} \)[/tex]
- [tex]\( r = \frac{3 \text{ inches}}{2} \)[/tex]
- [tex]\( r = 1.5 \text{ inches} \)[/tex]
3. Volume Formula for a Sphere:
- The formula for the volume [tex]\( V \)[/tex] of a sphere is [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].
4. Substitute the Radius into the Formula:
- [tex]\( V = \frac{4}{3} \pi (1.5)^3 \)[/tex]
5. Calculate the Volume:
- [tex]\( V = \frac{4}{3} \pi \times 1.5^3 \)[/tex]
- [tex]\( V = \frac{4}{3} \pi \times 3.375 \)[/tex]
- [tex]\( V \approx 14.137 \text{ cubic inches} \)[/tex]
6. Round to the Nearest Whole Number:
- [tex]\( 14.137 \text{ cubic inches} \)[/tex] rounded to the nearest whole number is [tex]\( 14 \text{ cubic inches} \)[/tex].
So, the volume of the baseball is approximately [tex]\( 14 \text{ cubic inches} \)[/tex].
Therefore, the correct answer is:
B. [tex]\( 14 \text{ in}^3 \)[/tex]
