Menu Close

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?
$$ \\ $$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
the side length is ((64))^(1/3) =4  imagine the cube as a box in front of you on  the table. the shortest path from the left  top front corner to the right bottom back  corner you can see by opening the lid. you  only have to follow the diagonal of the  rectangle formed by the lid and the back  side of the box  ⇒ answer is (√(4^2 +(2×4)^2 ))=4(√5)≈8.9cm
$$\mathrm{the}\:\mathrm{side}\:\mathrm{length}\:\mathrm{is}\:\sqrt[{\mathrm{3}}]{\mathrm{64}}=\mathrm{4} \\ $$$$\mathrm{imagine}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{as}\:\mathrm{a}\:\mathrm{box}\:\mathrm{in}\:\mathrm{front}\:\mathrm{of}\:\mathrm{you}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{table}.\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{path}\:\mathrm{from}\:\mathrm{the}\:\mathrm{left} \\ $$$$\mathrm{top}\:\mathrm{front}\:\mathrm{corner}\:\mathrm{to}\:\mathrm{the}\:\mathrm{right}\:\mathrm{bottom}\:\mathrm{back} \\ $$$$\mathrm{corner}\:\mathrm{you}\:\mathrm{can}\:\mathrm{see}\:\mathrm{by}\:\mathrm{opening}\:\mathrm{the}\:\mathrm{lid}.\:\mathrm{you} \\ $$$$\mathrm{only}\:\mathrm{have}\:\mathrm{to}\:\mathrm{follow}\:\mathrm{the}\:\mathrm{diagonal}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{rectangle}\:\mathrm{formed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{lid}\:\mathrm{and}\:\mathrm{the}\:\mathrm{back} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{box} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\sqrt{\mathrm{4}^{\mathrm{2}} +\left(\mathrm{2}×\mathrm{4}\right)^{\mathrm{2}} }=\mathrm{4}\sqrt{\mathrm{5}}\approx\mathrm{8}.\mathrm{9cm} \\ $$
Commented by iloveisrael last updated on 18/May/21
yes
$${yes} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *