Question

How will you arrange 12 cubes of equal length to form a cuboid of smallest surface area

Answer 1

lets take a few examples to begin with,
cuboid of 12=2*2*3 
S.A = 2(4+6+6) = 32 sq.units
 
cuboid of 12=6*2*1
S.A = 2(6+2+12)=40 sq.units

cuboid of 12=12*1*1
S.A = 2(12+1+12)=50 sq.units...
We see that for building the cuboid in such a way as to reduce S.A we must have factorization closest to its cube root factorization.

i.e 12 = ∛12 * ∛12 * ∛12
and ∛12 ≈ 2.28
Therefore the closest we can get to this configuration is in
12 = 2 * 2 * 3
Therefore the cuboid having side dimensions 2,2,3 of the cube block will have the lowest surface area i.e is 32 cube block squared units.