Estimation - Number of tennis balls that can fit in an Aircraft
Guess Estimate the number of tennis balls that can fit in an Aircraft
Clarifying Questions -
By Aircraft can we assume it to be a standard Boeing 747?
A) Yes, you can assume that.
Do we consider the aircraft with seats or without seats?
A) For the purpose of this question, let’s consider without seats.
Length of the Aircraft = 70 m long.
Width of the Aircraft = 6 m wide. (radius = 3 m)
The radius of a tennis ball = 3.3 cm
Volume of the Aircraft (considering it as a cylinder),
= Length x π x radius x radius
= 70 x π x 3 x 3 cubic meter
= 1978 cubic meter.
(The front and back are tapered, so there can be a 10% round off error)
The volume of a Tennis Ball,
~ 1.5e-4 cubic meter
Number of Tennis Balls that can be accommodated,
= (Volume of the Aircraft) / (Volume of the tennis ball)
= 1978 / 1.5e-4
= 13,186,666 tennis balls
Now, let’s take into consideration, “Best Packing Efficiency” of 74%
(Since tennis balls are spherical in shape, there will be some void gaps of some volume between the spheres)
Therefore, the number of tennis balls that can be packed efficiently in the aircraft,
= 74% of 13,186,666
= 9,758,132 tennis balls.
Now, let’s take, “Packing Efficiency” as 64% (When packed randomly)
The number of tennis balls in the aircraft, when packed randomly,
= 64% of 13,186,666
= 8,439,466 tennis balls.
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