A rectangular swimming pool has the same depth everywhere. The combined surface area of the floor of the pool and the four sides is 4800 square feet. What is the maximum volume of the swimming pool in cubic feet?
I think the greatest volume will be held by a cube (a square is a rectangle with = sides)
each side (there are 4) 4 x w x w
and the bottom w x w
total surface area 5 w^2 = 4800
w = depth = ~30.984 ft
volume = 30.9843 = ......... ft 3