[Campbell Biology P.1183] According to the principles of civil engineering discussed, if the ... | Practice Question

According to the principles of civil engineering discussed, if the weight a support needs to bear increases by a factor of 10, by what approximate factor must its diameter increase to maintain proportional strength?

  • A: It would need to increase by a factor of 10.
  • B: It would need to increase by a factor of approximately 3.16 (√10).
  • C: It would need to increase by a factor of 100.
  • D: It would need to remain the same.

Explanation

The strength of a support depends on its cross-sectional area, which increases with the square of its diameter Strength D^2 . If the weight to be supported increases by a factor of 10, then the strength must also increase by a factor of 10 to maintain proportional strength. For Strength D^2 to increase by 10, D^2 must increase by 10, so D must increase by √10, which is approximately 3.16.