How many tennis balls fit inside a Boeing 747?

Estimate how many standard tennis balls can fit inside the total interior passenger and cargo volume of a Boeing 747-400 aircraft.

Context

This is a classic volumetric Fermi problem testing geometry decomposition, packing efficiency factors, and fuselage spatial reasoning.

Clarifying questions to ask first

Is the airplane stripped empty of seats and galleys, or fully furnished with passenger seats?
Do we include lower belly cargo holds and upper deck? (Entire interior volume).

How to approach it

Estimate Boeing 747 dimensions: Fuselage length (~70m), cabin diameter (~6m), and cross-sectional internal volume
Deconstruct into Cylinder geometry: Volume = π × r² × h
Calculate volume of a single tennis ball (Sphere: 4/3 × π × r³ with diameter ~6.7 cm)
Apply 3D sphere packing efficiency factor (~64% random close packing or ~70% loose pack)
Account for fixtures, seating, luggage bins, and structural bulkheads

Framework: Usable Fuselage Volume (m³) × Sphere Packing Fraction (0.64) / Volume of Single Tennis Ball (m³)

Sample answer

Fuselage: Length ~60m usable, radius ~3m -> Volume = π × 3² × 60 = ~1,700 m³ (including cargo belly + upper deck = ~1,200 m³ usable void)
Tennis ball radius: ~3.3 cm (0.033m) -> Volume = 4/3 × π × (0.033)³ ≈ 0.00015 m³ (150 cm³)
Sphere packing efficiency: 64% (0.64)
Effective volume per ball = 0.00015 / 0.64 ≈ 0.000234 m³

Total usable void = 1,200 m³
Total balls = 1,200 m³ / 0.000234 m³ = ~5.1 Million tennis balls (Stripped empty: ~7M; furnished: ~5M)

Executive estimate: ~4.5 to 5.5 Million tennis balls fit inside a furnished Boeing 747 (up to ~7.5 Million if completely gutted to the aluminum frame).

What interviewers look for

Fuselage Geometry Estimation
Tennis Ball Volume Calculation
Sphere Packing Density Factor (~64%)
Interior Usable Space Deductions