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 :|

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

AB is the length of the diagonal, sorry.

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

The diagonal length is given by

s√3  = 44√3  = about 76.21cm

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

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

Yes i am an aclaimed artist.   LOL

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