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How do I find the length of the diagonal AB in a cube who's volume I know to be 85184cm^3? Not sure where to start :|

 Mar 4, 2015

Best Answer 

 #5
avatar+101769 
+10

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 Mar 4, 2015
 #1
avatar+101424 
+10

Is AB a side length....or.......the length of the diagonal  ???

 

                                                                                                                                                                                                                                       

 Mar 4, 2015
 #2
avatar+21 
+5

AB is the length of the diagonal, sorry.

 Mar 4, 2015
 #3
avatar+101424 
+10

Take the cube root of 85184........you should get 44....this is the side length, s

The diagonal length is given by

sāˆš3  = 44āˆš3  = about 76.21cm

 

 Mar 4, 2015
 #4
avatar+101769 
+5

side = $${{\mathtt{85\,184}}}^{\left\{{\frac{{\mathtt{1}}}{{\mathtt{3}}}}\right\}} = {\mathtt{43.999\: \!999\: \!999\: \!999\: \!99}}$$      =  44cm

 

diagonal of base =   $${\sqrt{{{\mathtt{44}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{44}}}^{{\mathtt{2}}}}} = {\mathtt{62.225\: \!396\: \!744\: \!416\: \!182\: \!1}}$$

 

diagonal of cube =  $${\sqrt{\left({{\mathtt{44}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{44}}}^{{\mathtt{2}}}\right){\mathtt{\,\small\textbf+\,}}{{\mathtt{44}}}^{{\mathtt{2}}}}} = {\mathtt{76.210\: \!235\: \!533\: \!030\: \!600\: \!9}}$$

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 Mar 4, 2015
 #5
avatar+101769 
+10
Best Answer

Melody Mar 4, 2015
 #6
avatar+101424 
+5

Nice pic, Melody......you have something in common with Picasso.......you're both into "cubism"....

 

  

 Mar 5, 2015
 #7
avatar+101769 
0

Yes i am an aclaimed artist.   LOL

 

I just haven't been discovered yet. :))

 Mar 5, 2015

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