When the size of an object were scaled up by a factor of 10 while retaining its present proportions, how would it affect the object's strength-to-weight ratio, and its surface area-to-volume ratio?

Question

When the size of an object were scaled up by a factor of 10 while retaining its present proportions, how would it affect the object's strength-to-weight ratio, and its surface area-to-volume ratio?

Answer 1

Strength-weight ratio for an object = strength/density. Since density is not dependent or shape or size, the SWR would not change.

Length is 1 dimension

Area is 2 dimensions

Volume is 3 dimensions

If the object was scaled up by a factor of 10:

Area would increase by 10² = 100

Volume would increase by 10³ = 1000

Therefor the area-to-volume ratio would change by 100:1000 or 1:10

Consider a sphere of radius 1 vs 10

Surface area = 4π r² = 4π (1) vs 4π (100) = 100 fold increase

Volume = 4/3π r³ = 4/3π(1) vs 4/3π(1000) = 1000 fold increase