When you are calculating the quantity of playpen balls needed to fill your front room it is very important to ensure that you know your geometry. So for example - my front room is about 3.5 metres square (or 12.25m2). If I wanted to fill this to 2 feet high (say .6m) then this would be a total cubic area of 7.35m3. Now - in order to work out the volume of balls we must take into account the air space between them when they pack together. I’ve been told that the optimum efficiency is 74%, the worst case is 60% and the reality is about 64%. As a result we will fill this 7.35m3 of space with a ball volume of 4.7m3 - or 4,700,000cm3.
This is where the distinction of diameter and radius come in. The first time I worked this out I popped 7.5 into the equation for the volume of a sphere (4/3 * pi * r3) and got 1767cm3. A quick division gives a requirement for around 2,600 balls to fill the space.
Tonight someone posed me with a problem that didn’t make sense so I revisited my calculations and realised my error. Popping in the radius of 3.75 gives me a value of 220cm3 - another quick division tells me I really need 21,300 balls to fill the space - a factor of 10 out.
This is also the difference between a just manageable £320 and a unrealistic £2800. A dream it shall remain then…. I still think there is a rental market.
You really need to find something else to fill your free time