What is the perimeter of an ellipse if the major axis is 30MM and the minor axis is 12MM?

Answer 1

72mm

Answer 2

A simple question with a horrendously complicated answer.

Short of carrying out elliptical integrals, the best I can suggest is the Ramanujan approximation according to which:

Perimeter = pi*{3(a + b) - sqrt[10ab + 3(a2 + b2)]} where a and b are the semi-major and semi-minor axes.

Substituting a = 15 mm and b = 6 mm gives

Perimeter = 69.04 mm.

A quick and easy, but roughly approximate method is as follows:

The ellipse is between a circle of diameter 30 mm and one of 12 mm. Averaging these two gives a diameter of 21 mm. A circle with a 21 mm diameter has a circumference (perimeter) of 65.97 mm.

Answer 3

28mm

Answer 4

283mm

Answer 5

49mm