Question

The mass of the shell of a bird egg (Mshell) scales with the overall mass of the egg (Megg) according to the following relationship: Mshell∝M^(1.132)egg = M to 1.132 power. In this question, you will determine the scaling relationship between the surface area of the egg shell and the mass of the egg.

Assuming a constant density, the size of an object scales as its mass raised to what power?

Answer 1

We have, Density = Mass/Volume

So, Mass = Density*Volume

Thus, constant density, Mass $\dpi{200} \propto$ Volume

But, volume $\dpi{200} \propto$ (size)^3,

So, mass $\dpi{200} \propto$ (size)^3

Or, size   $\dpi{200} \propto$ (mass)^1/3

Hence, at constant desity, the size of an object scales as its mass is raised to power of 1/3 or 0.34