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How can a cubic foot contain 230 feet of string?

Some excellent sibling replies but I think you've nailed it in terms of something that's easy to visualise

The same way your <2 meters body can contain 6 meters of intestines.

Same way your lungs have the surface area of a tennis court

The same way each of your cells contains 2 meters of DNA.

Capillaries are around the same width as the central bodies (soma) of neurons

They're thin.