Why pi?

My son asked a great question the other day: Why is pi between 3 and 4?

It's easy to show why 4 is an upper bound on pi, by inscribing a unit circle in a unit square.

But I have not yet been able to come up with an explanation of why 3 should be a lower bound for pi. Inscribing a square inside the unit circle gives 2.8+, and I suppose I could try higher-order polygons, but does anyone out there have a demonstration that will resonate with a fifth-grader?

Why pi?

My son asked a great question the other day: Why is pi between 3 and 4?

It's easy to show why 4 is an upper bound on pi, by inscribing a unit circle in a unit square.

But I have not yet been able to come up with an explanation of why 3 should be a lower bound for pi. Inscribing a square inside the unit circle gives 2.8+, and I suppose I could try higher-order polygons, but does anyone out there have a demonstration that will resonate with a fifth-grader?