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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

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 byiloveisrael last updated on 18/May/21

yes

$${yes} \\ $$

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