what is the volume of a baseball with a radius of 1.45 inches
The Correct Answer and Explanation is:
Correct Answer:
The volume VV of a baseball with a radius of 1.45 inches is approximately: V=43πr3=43π(1.45)3≈43π(3.052625)≈12.80 cubic inchesV = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (1.45)^3 \approx \frac{4}{3} \pi (3.052625) \approx 12.80 \text{ cubic inches}
Explanation:
To find the volume of a baseball, we treat it as a perfect sphere. The volume of a sphere is calculated using the standard mathematical formula: V=43πr3V = \frac{4}{3} \pi r^3
Where:
- VV is the volume,
- π\pi (pi) is a constant approximately equal to 3.1416,
- rr is the radius of the sphere.
In this problem, the radius rr is given as 1.45 inches. We begin by cubing the radius: r3=1.45×1.45×1.45=3.052625r^3 = 1.45 \times 1.45 \times 1.45 = 3.052625
Next, we multiply this result by 43\frac{4}{3} and then by π\pi: V=43×π×3.052625≈4.069×3.1416≈12.78 to 12.80 cubic inchesV = \frac{4}{3} \times \pi \times 3.052625 \approx 4.069 \times 3.1416 \approx 12.78 \text{ to } 12.80 \text{ cubic inches}
This gives us the volume of the baseball as approximately 12.80 cubic inches.
This calculation is essential for various practical applications. In sports science and manufacturing, knowing the exact volume helps in designing equipment, such as gloves and storage spaces. It also assists in determining material requirements and shipping volume. Furthermore, the precision of these calculations can affect performance in professional sports, where regulation size and weight are strictly enforced.
The formula for the volume of a sphere applies universally, so it’s also a helpful mathematical tool in other fields like astronomy, engineering, and architecture. This problem demonstrates how geometry applies to everyday objects and activities, offering insights into both their structure and function.
