Larger animals have sturdier bones than smaller animals. A mouse's skeleton is only a few percent of its body weight, compared t
o 16% for an elephant. To see why this must be so, recall, that the stress on the femur for a man standing on one leg is 1. 4% of the bone's tensile strength. Suppose we scale this man up by a factor of 10 in all dimensions, keeping the same body proportions. (assume that a 70 kg person has a femur with a cross-section area (of the compact bone) of 4. 8×10−4m2, a typical value. ).
cross-sectional area of the bone, a=4.8 \times 10^{-4} ~m^2
the factor of up-scaling the dimensions, s=10
Since we need to find the upscaled area having two degrees of the dimension therefore the scaling factor gets squared for the area being it in 2-dimensions.
