Finding the volume of a real egg if the volume of an egg shape(with different dimensions) on a graph is known

Question

Equation of the egg shown above:

If the volume of the egg show above is: $12.00405units^3$(found using calculus)

if the volume of a real egg is $55cm^3$

Is there anyway of finding out the volume of a real egg theoretically(i.e. only using the value obtained using calculus or find a scale factor for the volume of the egg in the graph and the volume of a real egg

Answer 1

You have used two parameters (u,v) and a constant $r$.

To me appears, variation of $r = ( 0.. 1) $ is incorrect, you assumed a constant value for $r_1$

You need to multiply by a factor.

$$ r_2 = r_1 \left( \frac{55}{ 12.00405}\right) ^ {1/3} $$

to get a bigger egg.