The strength of a rope is proportional to its cross-sectional area. If it were p

Question

The strength of a rope is proportional to its cross-sectional area. If it were pro-
portional to the volume, then making a rope twice as long would make it twice
as strong, which you hopefully agree is not the case. Similarly, the strength of a
muscle is proportional to its cross-sectional area, because this area is what deter-
mines the number of myofibrils which contract when the muscle applies a force.
Finally, the strength of a bone is also roughly proportional to cross-sectional area
(though the reason is not so obvious as in muscles.) In light of this, consider an
arm or a leg. If we make it 10 times as wide, 10 times as deep, and 10 times as
long, by what factor would its strength increase?

Explanation / Answer

The question already tells you that the length does not effect the strength. Making it 10 times as wide and deep. If we compare it to a rectangle with sides s1 and s2 with area s1*s2 and multiply by 10 each dimension we have 10s1*10s2 = 100*s1*s2. Thus the strength should increase by a factor of 100.

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