Question Number 74240 by ajfour last updated on 20/Nov/19
Commented by ajfour last updated on 21/Nov/19
$${Q}.\mathrm{73828}\:\:\:\left({If}\:{each}\:{face}\:{of}\:{outer}\right. \\ $$$${cube}\:{contains}\:{one}\:{corner}\:{of} \\ $$$${inner}\:{cube},\:{find}\:{range}\:{of}\:{s}/{a}. \\ $$$$\left(\boldsymbol{{s}}\:{being}\:{side}\:{length}\:{of}\:{inner}\:{cube},\right. \\ $$$$\left.\:\:{and}\:\boldsymbol{{a}}\:{that}\:{of}\:{outer}.\right) \\ $$
Commented by MJS last updated on 21/Nov/19
$$\mathrm{are}\:\mathrm{the}\:\mathrm{centers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cubes}\:\mathrm{identical}? \\ $$$$\mathrm{if}\:\mathrm{so},\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{the}\:\mathrm{inner}\:\mathrm{cube}\:\mathrm{are}\:\mathrm{located} \\ $$$$\mathrm{on}\:\mathrm{circles}\:\mathrm{on}\:\mathrm{the}\:\mathrm{faces}\:\mathrm{of}\:\mathrm{the}\:\mathrm{outer}\:\mathrm{one}... \\ $$
Commented by ajfour last updated on 21/Nov/19
$${The}\:{question}\:{asks}\:{for}\:{s}_{{min}} ,\:{Sir}. \\ $$$${a}=\mathrm{1}.\:{Besides}\:{each}\:{outer}\:{cube} \\ $$$${faces}\:{bearing}\:{one}\:{corner}\:{of} \\ $$$${inner}\:{cube},\:{the}\:{remaining}\:{two} \\ $$$${corners}\:{shouldn}'{t}\:{be}\:{outside}\:{the} \\ $$$${outer}\:{cube}. \\ $$$${In}\:{other}\:{words}. \\ $$$$\mathrm{Given}\:\mathrm{cube}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length}\:\mathrm{a}=\mathrm{1}. \\ $$$$\mathrm{Find}\:\mathrm{shortest}\:\mathrm{edge}\:\mathrm{length}\:\mathrm{s}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{cube}\:\mathrm{that}\:\mathrm{stretches}\:\mathrm{from}\:\mathrm{each} \\ $$$$\mathrm{face}\:\mathrm{of}\:\mathrm{the}\:\mathrm{outer}\:\mathrm{cube}\:\mathrm{to}\:\mathrm{its}\:\mathrm{oppo}- \\ $$$$\mathrm{site}\:\mathrm{face}. \\ $$
Answered by ajfour last updated on 21/Nov/19
