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
$$\mathrm{the}\:\mathrm{side}\:\mathrm{length}\:\mathrm{is}\:\sqrt[{\mathrm{3}}]{\mathrm{64}}=\mathrm{4} \\ $$$$\mathrm{imagine}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{as}\:\mathrm{a}\:\mathrm{box}\:\mathrm{in}\:\mathrm{front}\:\mathrm{of}\:\mathrm{you}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{table}.\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{path}\:\mathrm{from}\:\mathrm{the}\:\mathrm{left} \\ $$$$\mathrm{top}\:\mathrm{front}\:\mathrm{corner}\:\mathrm{to}\:\mathrm{the}\:\mathrm{right}\:\mathrm{bottom}\:\mathrm{back} \\ $$$$\mathrm{corner}\:\mathrm{you}\:\mathrm{can}\:\mathrm{see}\:\mathrm{by}\:\mathrm{opening}\:\mathrm{the}\:\mathrm{lid}.\:\mathrm{you} \\ $$$$\mathrm{only}\:\mathrm{have}\:\mathrm{to}\:\mathrm{follow}\:\mathrm{the}\:\mathrm{diagonal}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{rectangle}\:\mathrm{formed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{lid}\:\mathrm{and}\:\mathrm{the}\:\mathrm{back} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{box} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\sqrt{\mathrm{4}^{\mathrm{2}} +\left(\mathrm{2}×\mathrm{4}\right)^{\mathrm{2}} }=\mathrm{4}\sqrt{\mathrm{5}}\approx\mathrm{8}.\mathrm{9cm} \\ $$
Commented by iloveisrael last updated on 18/May/21
$${yes} \\ $$