Built from 974 recycled shipping containers, stadium 974 in Doha was the first temporary venue in World Cup history. If a standard container has an interior of 5.44m x 2.28m x 2.26m and a football has a radius of 11cm, how many can you fit per container? In all of the containers used in the stadium?

Scroll down for my solution!

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Solution

Container volume = 5.44 x 2.28 x 2.26 = 28.03 m³
Football volume = 4/3 x pi x r³ = 0.00558 m³ [using 0.11 m for the radius]

Method 1:
Container volume / football volume = 28.03 / 0.00558 = 5023 footballs

Method 2:
Not all of the container can be filled due to gaps between the spherical footballs. If packed randomly, the spheres take up 63.5% of the total space, and if packed optimally they can take up 74% of the available space.

Random packing: 0.635 x 28.03 = 17.8 m³ available, so 17.8 / 0.00558 = 3189 footballs

Optimal packing: 0.74 * 28.03 = 20.74 m³ available, so 20.74 / 0.00558 = 3717 footballs