Cut rectangular prism with planes parallel to faces

There is a rectangular prism 3 cm in length, 4 cm in width and 5 cm in height.

As for faces of this rectangular prism, the face of the rectangle with 3cm and 4cm side is set to face A, the face with 4cm and 5cm is set to face B and the face with 5cm and 3cm is set to face C.

Answer

Answer the following questions.

(1) Make small rectangular prisms by cutting with planes which are parallel to face A, face B and face C, once, once and twice respectively.

① Find the number of small rectangular prism.

② Find the sum total of the surface area of these small rectangular prisms.

Noted that the surface area of a rectangular prism is the sum total of the area of all the faces of the rectangular prism.

(2) This rectangular prism was cut with planes which are parallel to face A, face B and face C, X times, Y times and Z times respectively.

In this case, there are 90 small rectangular prisms made and the sum total of the surface area of these rectangular prisms was 462 cm². Find the number applicable to X, Y, and Z.