The rectangular prism has a volume of length x width x height = 10 in x 9 in x 9 in = 810 cubic inches.
The pyramid that is cut from the prism has a volume of (1/3) x base area x height = (1/3) x 9 in² x 2 in = 6 in³.
The pyramid that is added to the opposite base has a volume of (1/3) x base area x height = (1/3) x 9 in² x 3 in = 9 in³.
The composite figure is formed by removing a pyramid with volume 6 in³ from the rectangular prism and adding a pyramid with volume 9 in³ to the opposite base. The resulting figure is still a rectangular prism, with the same length and width, but a slightly different height.
The height of the rectangular prism is reduced by 2 inches (the height of the pyramid that was cut), and then increased by 3 inches (the height of the pyramid that was added). So, the new height of the rectangular prism is:
9 in - 2 in + 3 in = 10 in
The volume of the composite figure is then:
Volume = length x width x height = 10 in x 9 in x 10 in = 900 cubic inches.
Therefore, the volume of the composite figure is 900 cubic inches.