How Many Tennis Balls Can You Fit in an Airplane?
How Many Tennis Balls Can You Fit in an Airplane?
This question isn’t about finding an exact number but about showcasing your problem-solving approach. Here's how you can tackle it logically:
1. Estimate the Volume of a Tennis Ball
A tennis ball has a diameter of about 2.5 inches. Using the formula for the volume of a sphere:
[
V = \frac{4}{3} \pi r^3
]
where (r = 1.25) inches, the volume is approximately 8 cubic inches.
2. Estimate the Volume of the Airplane
Consider a commercial airplane like a Boeing 747. The cargo hold might measure roughly 150 feet long, 30 feet wide, and 20 feet high, equating to a volume of:
[
150 \times 30 \times 20 = 90,000 \text{ cubic feet.}
]
Convert to cubic inches (1 cubic foot = 1,728 cubic inches):
[
90,000 \times 1,728 = 155,520,000 \text{ cubic inches.}
]
3. Account for Packing Efficiency
Tennis balls won’t fit perfectly due to their spherical shape. Typically, packing efficiency for spheres is around 70%. Adjust the usable volume:
[
155,520,000 \times 0.7 = 108,864,000 \text{ cubic inches.}
]
4. Divide the Volumes
Divide the usable cargo volume by the volume of one tennis ball:
[
\frac{108,864,000}{8} = 13,608,000 \text{ tennis balls.}
]
Final Answer
Approximately 13.6 million tennis balls could fit in a commercial airplane like a Boeing 747, assuming optimal packing and no other cargo.
The purpose of this calculation is to demonstrate logical thinking, not to provide a definitive figure. Explaining your assumptions and method clearly is the key to impressing your interviewer.