An open rectangular box with a volume of 42 ft3 has a square base. Express the surface area S of the box in terms of the length x of one side of the base?

Question

anonymous · Answer

Do you know Volume formula?
Surface Area formula?

anonymous · Answer

V=lwh
SA=2lw+2lh+2hw

anonymous · Answer

Since base is square with side x, and let y is the height:
V = x² y   =  42 ft³

anonymous · Answer

SA=4x^2+2xy

anonymous · Answer

V     = x² y = 42 ft³
->           y =  42/ x²                  (1)  
SA =  1 bottom + 4 sides
       =   x²            + 4 ( xy)        (2)
Now plug  (1) into (2) to get SA with respect to x value:

anonymous · Answer

LOL, I forgot it was topless, haha. Thank you!