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-

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?

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 by iloveisrael last updated on 18/May/21

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