# How to measure an egg surface in square centimeter?

I just got a brain challenge from my physics teacher to measure the surface of an egg as precisely as possible when leaving the egg in one piece.

my idea was to take the skin off and weight it' then break a square out of the skin, measure the square's surface and weight it also, and the multiply and you know the rest...

It ended up to 50 and something square cm but it sure wasn't precise.

Also, I'm a 9th grader so if possible don't give me hard equations to solve,

Thanks

me

Relevance

I have gone back to look at this question. Contrary to what others have said, this question has been examined over and over and there is a substantial literature on it. The size and shape of eggs is very interesting to people in the poultry industry, and those who must develop machinery that interacts with eggs, as well as environmentalists and others.

There are several problems here clearly. One is, there is no uniform shape to an egg. Different animals and different species produce different-shaped eggs.

The second is, there is no easy formula available for an egg shape that is well-known.

That said, there are lots of approximation and estimation methods available, as well as lots of experimental data and tables for different kinds of eggs.

In general, for eggs that are rotationally symmetric about an axis, the surface area

A= 2*pi* {int from a to b} y(x) * sqrt[1+y'(x)] dx

where y(x) is the curve describing the boundary of the egg,

a<=x<=b. If y(x) is analytic, then this integral can be done analytically. If not, it can be done numerically, as done by one of the references.

In the case of hen's eggs, T. C. Carter (1968) produced a 3 parameter model for computing surface area ("The hen's egg: A mathematical model with three parameters", Brit. Poulty Sci. 9, 165-171, 1968). In 1949, Romanoff, A. L., and A. J. Romanoff published a book with many formulae and approximation methods for egg surface areas called "The

avian egg" (John Wiley & Sons, Inc., New York, 1949).

One of the references approximates the egg as a prolate spheroid to compute its surface area.

Some of the references produce empirical formulae for the volume and surface areas of various shapes of eggs. For example, the abstract by V. G. Narushin in the references presents the presumably empirically fit-model of egg surface area, S, calculated as S = (3.155 – 0.0136L + 0.0115B)LB, in which both L and B are taken in millimeters (obviously there is a problem with the units here).

One of the other references presents some empirically-derived formulae relating weight W of the egg to its surface area A that appear to fit quite closely (for example, A=4.835*W^0.662).

I think that once you decide exactly what sort of egg you are interested in, there is a wealth of material available to investigate this further.

Source(s):

http://elibrary.unm.edu/sora/Condor/file…

http://elibrary.unm.edu/sora/Condor/file…

http://www.sidwell.edu/us/science/vlb5/L…

http://mathforum.org/library/drmath/view…

http://mathforum.org/library/drmath/view…

http://uteach.utexas.edu/ResearchMethods…

http://chickscope.beckman.uiuc.edu/explo…

http://www.poultryscience.org/ps/abs/05/…