Question 404190
a) Let s = side of a cube. Then {{{d = sqrt(s^2 + s^2 +s^2) = sqrt(3s^2) = sqrt(3)*s}}}, or {{{s  =d/sqrt(3)}}}.
==> {{{TSA =  6*s^2 = 6*(d^2/3) = 2d^2}}}


b) {{{V = s^3 = (d/sqrt(3))^3 = d^3/(3sqrt(3)) = (d^3/(3sqrt(3)))*(sqrt(3)/sqrt(3)) = (sqrt(3)d^3)/9}}}