Surface Area of an Egg

Date: 02/28/2001 at 05:09:05
From: Sean
Subject: Surface area of an egg

Hi -

How do you find the surface area of an egg?

This is very important.

Date: 02/28/2001 at 07:53:35
From: Doctor Jerry
Subject: Re: Surface area of an egg

Hi Sean,

Using calculus, one can find the surface area of a surface IF the 
surface can be described by an equation or by a parametric equations.  
The "egg shape," however, has no standard, well-known equation. If you 
provide the equation, I can tell you how to calculate its area. I 
imagine that at least approximately, the surface of an egg is a 
"surface of revolution," which makes it easier. However, one must give 
an equation of the curve which, when rotated about the line of 
symmetry of the egg, generates the surface.

If this curve were described by y = f(x), a <= x <= b, the area of the 
generated surface would be

   int(x=a,x=b,2*pi*f(x)*sqrt(1+f'(x)^2)*dx).

Often, such integrals must be done numerically.

Jerry

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/