Arc length

A slice is a fraction of the whole circle, and the angle says which fraction. A full turn is 360°, so 270° is 270 out of 360 — that is 3/4 of the circle.

Now the whole circle. All the way around is 2 × π × r: 2 × 3.14 × 6 = 37.68 cm.

Then take the slice's share of it: 3/4 of 37.68 is 28.26.

So the curved edge is 28.26 cm.