P28 Question 3: Cut a cuboid into more than one pyramid along the diagonal of three adjacent faces, and find the ratio of the volume of the pyramid to the volume of other geometric bodies?

Solution: If the length, width and height of a cuboid are a, b and c respectively, the truncated pyramid volume is1/3×1/2× ABC =1/6abc, and the remaining geometric volume is abc- 1/6abc=5/6abc.

Question 4: There is water in the triangular prism container, and the side AA 1=8. If the side AA 1B 1B is placed horizontally, and the liquid level just passes through the midpoint of AC, BC, A 1c 1, then

Analysis: When the side of triangular prism AA 1B 1B is placed horizontally, the liquid part is a quadrangular prism, the height of which is higher than that of the original triangular prism, and the length of the side AA 1 is 8.

Solution: Let the midpoint of AC and BC sides be E and F respectively, and the liquid level height is H when the bottom ABC is placed horizontally.

SABFE×8=SABC×h, and from the condition that SABFE:SABC=3:4 and the liquid volumes in the two States are equal, it can be obtained that ∴h=6.