Question

for a button to fit through its buttonhole the hole needs to be the size of the buttons diameter. what size buttonhole is needed for a bottom with the circumference of 7.38cm

Answer 1

Circumference; C = π2r
Diameter; D = 2r

So then ...
C = πD

7.38 = πD
7.38 / π = D

2.35 cm = D