Larger animals have sturdier bones than smaller animals. A mouse's skeleton is only a few percent of its body weight, compared to 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 person has a femur with a cross-section area (of the cortical bone) of , a typical value.)
A: Both the inside and outside diameter of the femur, the region of cortical bone, will increase by a factor of 10. What will be the new cross-section area?
B: The man's body will increase by a factor of 10 in each dimension. What will be his new mass?
C: If the scaled-up man now stands on one leg, what fraction of the tensile strength is the stress on the femur?