A rectangular box is designed to have a square base and an open top. The volume is to be 1372cm3. What is the minimum surface area that suc

My 'stab' at it:

Surface area will be the are of the square bottom  PLUS the 4 rectangular sides

s = side width and square side

square area = s^2

h = height of rectngle area   surface area of the 4 sides =  s x h x 4 = 4 sh

4sh + s^2  = area

Volume = s x h x s = s^2h = 1372  cm^3

h = 1372/s^2

4 s 1372/s^2 + s^2 = area

5488/s + s^2 = area

s^2 + 5488 (s^-1) = area      Take derivative and set = 0 to find the minimum  (not SURE about this step)

2s - 5488 s^-2 = 0

5488 s^-2 = 2s

5488 = 2 s^3

2744 = s^3     s =  14            and s x h x s = 1372     then h = 7   

   surface area then = 14 x14 + 4 x 7 x 14 = 196+4*7*14 = 588  cm^2