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Question-189563




Question Number 189563 by Rupesh123 last updated on 18/Mar/23
Answered by FelipeLz last updated on 19/Mar/23
V = (r_1 +2)×(r_2 +2)×(r_3 +2) = r_1 r_2 r_3 +2(r_1 r_2 +r_1 r_3 +r_2 r_3 )+4(r_1 +r_2 +r_3 )+8   r_1 r_2 r_3  = (6/(10))  r_1 r_2 +r_1 r_3 +r_2 r_3  = ((29)/(10))  r_1 +r_2 +r_3  = ((39)/(10))  V = (6/(10))+2×((29)/(10))+4×((39)/(10))+8  V = ((220)/(10))+8 = 30
$${V}\:=\:\left({r}_{\mathrm{1}} +\mathrm{2}\right)×\left({r}_{\mathrm{2}} +\mathrm{2}\right)×\left({r}_{\mathrm{3}} +\mathrm{2}\right)\:=\:{r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} +\mathrm{2}\left({r}_{\mathrm{1}} {r}_{\mathrm{2}} +{r}_{\mathrm{1}} {r}_{\mathrm{3}} +{r}_{\mathrm{2}} {r}_{\mathrm{3}} \right)+\mathrm{4}\left({r}_{\mathrm{1}} +{r}_{\mathrm{2}} +{r}_{\mathrm{3}} \right)+\mathrm{8}\: \\ $$$${r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} \:=\:\frac{\mathrm{6}}{\mathrm{10}} \\ $$$${r}_{\mathrm{1}} {r}_{\mathrm{2}} +{r}_{\mathrm{1}} {r}_{\mathrm{3}} +{r}_{\mathrm{2}} {r}_{\mathrm{3}} \:=\:\frac{\mathrm{29}}{\mathrm{10}} \\ $$$${r}_{\mathrm{1}} +{r}_{\mathrm{2}} +{r}_{\mathrm{3}} \:=\:\frac{\mathrm{39}}{\mathrm{10}} \\ $$$${V}\:=\:\frac{\mathrm{6}}{\mathrm{10}}+\mathrm{2}×\frac{\mathrm{29}}{\mathrm{10}}+\mathrm{4}×\frac{\mathrm{39}}{\mathrm{10}}+\mathrm{8} \\ $$$${V}\:=\:\frac{\mathrm{220}}{\mathrm{10}}+\mathrm{8}\:=\:\mathrm{30}\: \\ $$
Commented by Rupesh123 last updated on 19/Mar/23
Excellent!
Answered by manxsol last updated on 19/Mar/23
r_1 r_2 r_3 =(6/(10))=V_i   (2r_1 )(2r_2 )(2r_3 )=((48)/(10))=((24)/5)=V_f
$${r}_{\mathrm{1}} {r}_{\mathrm{2}} {r}_{\mathrm{3}} =\frac{\mathrm{6}}{\mathrm{10}}={V}_{{i}} \\ $$$$\left(\mathrm{2}{r}_{\mathrm{1}} \right)\left(\mathrm{2}{r}_{\mathrm{2}} \right)\left(\mathrm{2}{r}_{\mathrm{3}} \right)=\frac{\mathrm{48}}{\mathrm{10}}=\frac{\mathrm{24}}{\mathrm{5}}={V}_{{f}} \\ $$

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