volume is given to be 4.5 m^3
v = length x width x height
v = lwh
want everything in one variable w
given that;
l = 2w
using volume...
h = 4.5 / lw
h = 4.5 / 2w^2
surface area = wl + 2hl + 2wh
sub for length and height
s = 2w^2 + 9/w + 4.5/w
s = 2w^2 + 13.5/w
derivative s
s' = 4w - 13.5/w^2
0 = 4w - 13.5/w^2
13.5/w^2 = 4w
13.5 = 4w^3
13.5/4 = w^3
3.375 = w^3
cube root
1.5 meters = w
then the length = 2(1.5) = 3 meters
height = 4.5/(3*1.5) = 1 meter
