We have to calculate the size of a buttonhole if we know that it needs to be the size of the button`s diameter. We know also a circumference of the button: C = 9.42 cm. Formula for calculating the circumference is: C = 2 r Pi = d Pi. Pi is approximately 3.14. So 9.42 = d 3.14; d = 9.42 : 3.14; d = 3 cm. Answer: The size of the buttonhole has to be 3 cm.