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Question Number 141395 by iloveisrael last updated on 18/May/21

$$$$ A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length? \n

Answered by MJS_new last updated on 18/May/21

$$\mathrm{the}\mathrm{side}\mathrm{length}\mathrm{is}\sqrt[3]{64}=4$$ $$\mathrm{imagine}\mathrm{the}\mathrm{cube}\mathrm{as}\mathrm{a}\mathrm{box}\mathrm{in}\mathrm{front}\mathrm{of}\mathrm{you}\mathrm{on}$$ $$\mathrm{the}\mathrm{table}.\mathrm{the}\mathrm{shortest}\mathrm{path}\mathrm{from}\mathrm{the}\mathrm{left}$$ $$\mathrm{top}\mathrm{front}\mathrm{corner}\mathrm{to}\mathrm{the}\mathrm{right}\mathrm{bottom}\mathrm{back}$$ $$\mathrm{corner}\mathrm{you}\mathrm{can}\mathrm{see}\mathrm{by}\mathrm{opening}\mathrm{the}\mathrm{lid}.\mathrm{you}$$ $$\mathrm{only}\mathrm{have}\mathrm{to}\mathrm{follow}\mathrm{the}\mathrm{diagonal}\mathrm{of}\mathrm{the}$$ $$\mathrm{rectangle}\mathrm{formed}\mathrm{by}\mathrm{the}\mathrm{lid}\mathrm{and}\mathrm{the}\mathrm{back}$$ $$\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{box}$$ $$\Rightarrow \mathrm{answer}\mathrm{is}\sqrt{4^2+{\left(2\times 4\right)}^2}=4\sqrt{5}\approx 8.9\mathrm{cm}$$

Commented byiloveisrael last updated on 18/May/21

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