A cuboid can just be cut into two cubes. After cutting, the surface area increases by 18 square decimeters. What's the volume of this cuboid?

A cuboid can just be cut into two cubes. After cutting, the surface area increases by 18 square decimeters. What's the volume of this cuboid?

After cutting, add two sides, both are square, with a total area of 18 square decimeters, each 9 square decimeters, so the edge length of the cube is 3 decimeters
18 △ 2 = 9 square decimeter = 3 × 3
Volume of a cube: 3 × 3 × 3 = 27 cubic decimeters
Original cuboid volume = 2 cubes volume = 27 × 2 = 54 cubic decimeters