Exemple: In 3 pyramid P-ABC, PA ＝ 3, PB ＝ 4, PC ＝ 5. A1, B1, C1 is respectively on PA, PB, PC, and PA1 ＝ 2, PB1 ＝ 3, criterion the bulk of 3 pyramid P-A1B1C1 and polyhedron A1B1C1-ABC is ( )
A, 1:3B, 1:4C, 1:5D, 1:6
Apparent, polyhedron A1B1C1-ABC is not the regular graph on traditional sense, want to beg its bulk to have a lot of and unknown factor, consequently difficulty cans be imagined. If regard it,be 3 pyramid P-ABC and the difference of 3 pyramid P-A1B1C1. Beg what starting point puts in latter take, the question is much simpler. If be opposite a few need to involve but the quantity that the condition did not give out again, might as well bold introduce two character, criterion problem but be readily solved.
Solution: Make PBC of AH perpendicular plane at H, a1H1⊥ planar PBC at H, criterion P1, H, H1 at 3 o'clock in all line.
Set ∠BPC ＝ γ , ∠APH ＝ β , criterion AH ＝ PAsinβ , a1H1 ＝ PA1sinβ
Then PB1C1·A1H1 of △ of VP-A1B1C1 ＝ 1/3S
＝ 1/6PB1·PC1sinγsinβ
＝ 1/6×2×3×2sinγsinβ
＝ 2sinγsinβ
∴ VP-ABC:VP-A1B1C1 ＝ 2sinγsinβ:102sinγsinβ=1:5
∴ VP-A1B1C1: 1:4 of ＝ of 1B1C1-ABC of belch beautiful 錋
Reason should choose B.
You look, we introduce parameter γ , β , make the problem obtains solution smoothly, is actually set and do not beg. When to introduce parameter, introduce what parameter, this kind of consciousness and ability, want education of the act carefully in practicing at ordinary times, what in an attempt to applies is clever, put its heart.
