Some maths with Social Distancing

As part of the advice of what to do to avoid spreading coronavirus, the BBC has some little graphics.  The one about social distancing (where we were advised to keep 2m apart) is this:

Is this to scale?

If we lie the chap down, and assume he is about 6 ft tall, then the circle appears to have a diameter of about 2 metres.

But hold on, we have to be 2m _away_ from other people: I mustn’t just be this distance away from others but should be twice that amount.  The first diagram here is bad, the second is good.

If I remove the major arc of the circle, suddenly this graphic makes sense:

The artist was thinking of us as Subbuteo figures

(Royalty-free image from Shutterstock)

This then leads to the question of how many people could fit in a room, obeying the requirement of being 2m apart.

My first thought was that this was a ‘packing’ problem, and for a 2m by 5m room I produced this diagram:

But we aren’t actually Subbuteo figures, so it’s fine for our ‘base’ to overlap the edge of the room.  In fact, we can have at least 6 people in the room:

Further questions:

1. Can we have more than 6 people in this room?
2. Is it possible for them to get into the room without violating each other’s space?  Does it depend on where the door is?
3. How many people will fit in rooms of other dimensions?
4. What is the smallest room that will fit a particular number of people?