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Question Number 119463 by TANMAY PANACEA last updated on 24/Oct/20
one cube of side length 3cm is painted by three colour  say (red blue and black) opposte face same colour  Now cube is cut into 27 small cube  i)How many cube has three face coloured  ii)How many cube two face coloured  iii)How many cube  has no colour in its face
$${one}\:{cube}\:{of}\:{side}\:{length}\:\mathrm{3}{cm}\:{is}\:{painted}\:{by}\:{three}\:{colour} \\ $$$${say}\:\left({red}\:{blue}\:{and}\:{black}\right)\:{opposte}\:{face}\:{same}\:{colour} \\ $$$${Now}\:{cube}\:{is}\:{cut}\:{into}\:\mathrm{27}\:{small}\:{cube} \\ $$$$\left.{i}\right){How}\:{many}\:{cube}\:{has}\:{three}\:{face}\:{coloured} \\ $$$$\left.{ii}\right){How}\:{many}\:{cube}\:{two}\:{face}\:{coloured} \\ $$$$\left.{iii}\right){How}\:{many}\:{cube}\:\:{has}\:{no}\:{colour}\:{in}\:{its}\:{face} \\ $$
Commented by TANMAY PANACEA last updated on 25/Oct/20
Commented by TANMAY PANACEA last updated on 25/Oct/20
1)three face coloured=8 (cube at corner)  2)see top most layer and bottom most layer  4×2=8 cube two face coloured.  middle layer 4 cube of corner  so total =8+4=12  3)see topmost and bottom most face centred cube  one face coloured and middle layer 4 cube  =2+4=6 cube one face coloured  4)noface coloured=1 cube  so  three(o3)face coloured=8  two face coloured=12  one face coloured=6  no face coloured=1  8+12+6+1=27
$$\left.\mathrm{1}\right){three}\:{face}\:{coloured}=\mathrm{8}\:\left({cube}\:{at}\:{corner}\right) \\ $$$$\left.\mathrm{2}\right){see}\:{top}\:{most}\:{layer}\:{and}\:{bottom}\:{most}\:{layer} \\ $$$$\mathrm{4}×\mathrm{2}=\mathrm{8}\:{cube}\:{two}\:{face}\:{coloured}. \\ $$$${middle}\:{layer}\:\mathrm{4}\:{cube}\:{of}\:{corner} \\ $$$${so}\:{total}\:=\mathrm{8}+\mathrm{4}=\mathrm{12} \\ $$$$\left.\mathrm{3}\right){see}\:{topmost}\:{and}\:{bottom}\:{most}\:{face}\:{centred}\:{cube} \\ $$$${one}\:{face}\:{coloured}\:{and}\:{middle}\:{layer}\:\mathrm{4}\:{cube} \\ $$$$=\mathrm{2}+\mathrm{4}=\mathrm{6}\:{cube}\:{one}\:{face}\:{coloured} \\ $$$$\left.\mathrm{4}\right){noface}\:{coloured}=\mathrm{1}\:{cube} \\ $$$$\boldsymbol{{so}} \\ $$$$\boldsymbol{{three}}\left(\boldsymbol{{o}}\mathrm{3}\right)\boldsymbol{{face}}\:\boldsymbol{{coloured}}=\mathrm{8} \\ $$$$\boldsymbol{{two}}\:\boldsymbol{{face}}\:\boldsymbol{{coloured}}=\mathrm{12} \\ $$$$\boldsymbol{{one}}\:\boldsymbol{{face}}\:\boldsymbol{{coloured}}=\mathrm{6} \\ $$$$\boldsymbol{{no}}\:\boldsymbol{{face}}\:\boldsymbol{{coloured}}=\mathrm{1} \\ $$$$\mathrm{8}+\mathrm{12}+\mathrm{6}+\mathrm{1}=\mathrm{27}\: \\ $$
Answered by som(math1967) last updated on 25/Oct/20
i)8 cubes  ii)8 cubes  iii) 1cube
$$\left.\mathrm{i}\right)\mathrm{8}\:\mathrm{cubes} \\ $$$$\left.\mathrm{ii}\right)\mathrm{8}\:\mathrm{cubes} \\ $$$$\left.\mathrm{iii}\right)\:\mathrm{1cube} \\ $$$$ \\ $$
Commented by som(math1967) last updated on 25/Oct/20
Thik bollam?
$$\mathrm{Thik}\:\mathrm{bollam}? \\ $$

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