This is a classic Fermi problem that requires estimation and logical breakdown. To solve it, we need to make several assumptions:
- Type of Airplane: We'll assume a standard domestic passenger jet (e.g., Boeing 737 or Airbus A320) with an approximate seating capacity of 150 people. This helps us estimate the internal volume.
- Empty vs. Occupied: We'll assume the plane is completely empty – no passengers, luggage, or crew – to maximize available space.
- Fillable Space: We'll consider only the main cabin, cockpit, and cargo hold. We will exclude external areas like wings and engines.
- Ball Properties: A standard tennis ball has a diameter of about 2.6 inches (0.066 meters) and a volume of approximately 0.000148 cubic meters.
Calculation Steps:
- Estimate Airplane Volume: A rough estimate for the interior volume of a 737-sized aircraft is around 150-200 cubic meters. Let's use 175 cubic meters as an average.
- Calculate Tennis Ball Volume: Using the diameter, the volume of a single tennis ball is approximately 0.000148 m³.
- Initial Calculation (Ignoring Packing Inefficiency): Divide the airplane's volume by the tennis ball's volume: 175 m³ / 0.000148 m³ ≈ 1,182,432 balls.
- Account for Packing Inefficiency: Spheres cannot perfectly fill a space. The most efficient packing for spheres (random close packing) achieves about 64% efficiency. Therefore, we multiply our initial estimate by this factor: 1,182,432 * 0.64 ≈ 756,756 balls.
Conclusion: A reasonable estimate is that approximately 750,000 to 800,000 tennis balls could fit inside a standard domestic passenger airplane, assuming it's empty and we only fill the interior spaces.
Agoda