Since the volume of the cube is 1 ft^3 then each side of the cube has to be 1 ft since 1ft*1ft*1ft=1ft^3
Now since all 6 sides of a cube have equal sides, the surface area would just be one area of 1 face*6.
Now we know the side lengths the area of 1 face is 1ft*1ft=1ft^2
Now:
1ft^2*6=6ft^2.
Yes you got the answer correct, but I still want you to read the explanation to see how I got the answer.