How many ping pong balls can fit in a helicopter?

This question might seem silly at first, but it's actually a popular type of question known as a Fermi problem, named after physicist Enrico Fermi. These are estimation problems designed to test your problem-solving skills, logical thinking, and ability to make reasonable assumptions.

To handle this question, you should break the problem down into manageable parts:

1. First, estimate the size of the helicopter. This would typically be considered from the inside as we want to fill it with ping-pong balls.
2. Next, estimate the volume of a ping-pong ball.
3. Finally, relate these two quantities to estimate how many balls could fit inside the helicopter.

This kind of question isn't necessarily looking for a correct answer - actually, being able to give an immediately accurate answer might indicate you knew the answer in advance, which defeats the question's purpose. Rather, it tests your ability to think through a problem logically and creatively under pressure.

The volume of a helicopter's interior would vary greatly, but for this estimation let's say it's about 10 cubic meters (roughly the size of a small van).

A ping-pong ball is about 4cm in diameter, so its radius is 2cm (or 0.02 meters). Using the formula for the volume of a sphere which is 4/3 * pi * r^3, the volume of one ping-pong ball comes out to be about 0.000033 cubic meters.

This would suggest you could fit about 300,000 ping-pong balls in a helicopter, but this is assuming the balls can perfectly fill the space which is impossible. If we consider the packing efficiency of sphere which is roughly 0.74, we need to adjust our estimate. So, our final estimation on how many ping-pong balls can fit in a helicopter would be 0.74 * 300,000, which equals to approximately 222,000 balls.

Let's assume for simplicity that a helicopter has a roughly cylindrical shape, and ballpark its dimensions at about a 2 meter radius and 3 meter height. So, the volume of the helicopter would be the volume of a cylinder, which is pi * r^2 * h = approximately 37.7 cubic meters.

Ping pong balls, on the other hand, are spheres of about 2 cm radius. Therefore, the volume of one ping-pong ball is 4/3 * pi * r^3 = approximately 0.0000335 cubic meters.

Dividing the volume of the helicopter by the volume of a single ping-pong ball gives us the total possible number of ping-pong balls. But, considering that spheres have a packing efficiency of about 0.74 (since they can't stack perfectly), adjust this total number by that factor. The final estimation then comes close to 850,000 ping-pong balls.