The ratio of the lengths of corresponding parts in two similar solids is 4:1?

What is the ratio of their surface area?

Answer:
Imagine if we were talking about 2 cubes. The biggest would have a surface area of 4s*4s*6 = 96s*s
the smallest would have a surface area of s*s*6 = 6s*s

so that ratio would be 16:1

If they were spheres, the surface area of the big one would be 4(pi)(4s)(4s) versus 4(pi)*s*s*s
so 64(pi)*s*s*s versus 4(pi)*s*s*s
again we have a 16:1 ratio
If length scales as N ratio then N^2 for area ratio and N^3 for volume ratio.

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