# 3D Shapes & Scale

Write an explanation of ONE of the following question: (your explanation should be in paragraph form and should be written for a reader who is completely unfamiliar with area/volume scale factors and the square-cube law)

1) Why can aquatic animals grow so much larger than land animals?
2) Why are godzilla and king kong type monsters physically impossible?
3) Why is it impossible for an ant to fall to its death?

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1. 1) Archimedes holds you up in the ocean. Water is about 800 times as dense as air. In fact it is about the density of most animals, including people and whales. Therefore when you are in the water you need to exert very little force to hold yourself up. Similarly a whale is about neutrally buoyant. On land, a whale would need fantastic legs to get around. In the ocean, no problem.
for similar objects:

weight = constant * length cubed
strength of column or bone = constant * length square
so
ratio of weight to strength = L^3/L^2 = L
twice as long, half as strong.

I guess that answers the second two now that I see them.

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posted by Damon
2. by the way the ant is not only immensely strong for its weight but that A - k L^2 ratio means it has a big surface area for its length. Therefore it's terminal velocity is much lower than yours.

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posted by Damon
3. I mean big surface area for its weight

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posted by Damon

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