Question

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?

Answer 1

Do you know Volume formula?
Surface Area formula?

Answer 2

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

Answer 3

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

Answer 4

SA=4x^2+2xy

Answer 5

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:

Answer 6

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