c Use Part A to find how much weight his legs should support in terms of average people and compare it to how much they actually must support, as found in Part B.
A
a 100 times
B
b 1000 times
C
c His weight is 1000 times the weight of an average person, but his bones can support only 600 times the weight of an average person.
Practice makes perfect
a Stories say that Paul Bunyan is 10 times as tall as the average human and we are to assume that his bone structure is proportional to that of ordinary people. Paul's height tells us that the scale factor of him to average people is 1:10. Let's use the Areas and Volumes of Similar Solids Theorem to recall the relationship between the scale factor and area.
Areas and Volumes of Similar Solids Theorem
If the scale factor of two similar solids is ab or a:b, then the ratio of their areas is a^2b^2 or a^2:b^2.
The strength of bones is proportional to the area of their cross section. To get that area and therefore the strength of bones, we will square the scale factor.
Paul Bunyan's weight is 1000 times that of an average persons.
c Human leg bones can support about 6 times the average person's weight. If Paul Bunyan is proportional to humans then the same can be said about him. As found in Part A, we know his bones are 100 times as strong as those of the average human. So we will multiply it by 6 to get how much he should weigh.
l
6 * Bone strength = Average person's weight
6 * 100 = 600
By this logic Paul's bones should only be able to support 600 times the average person's weight. However, we found in Part B that they actually support 1000 times the average person's weight, so Paul Bunyan cannot exist with a bone structure proportional to that of an ordinary person.
