ᠬᠤᠷᠢᠨ ᠶᠢᠰᠤᠳᠤᠭᠡᠷ ᠪᠦᠯᠦᠭ ᠲᠤᠰᠬᠠᠯᠳᠠ ᠪᠠ ᠬᠠᠷᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 2） .pdf

ᠬᠣᠷ ᠢ ᠶᠢ ᠰᠤᠳᠤᠭ ᠡᠷ ᠪᠥᠯ ᠥᠭ ᠦᠨ ᠪ ᠠᠢᠴ ᠠᠭᠠᠯᠲᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ ᠃ ︵ ᠰᠡᠲᠤᠪ ᠪᠦ ᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ ︶ 1. ᠨᠢᠭᠡ ᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢ ᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷᠤᠭ ᠨᠢ ᠵᠢᠷᠤ ᠭ 1 ᠮᠡᠳᠤ ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢ ᠨ ᠪ ᠡᠶ ᠡ ᠨᠢ ( ) A. ᠪᠦᠭᠡᠷᠡ ᠩᠬᠡᠢ ᠪᠠᠭᠠᠨ ᠠ B. ᠱᠤᠷᠤᠯ ᠵᠢᠨ C. ᠬᠤᠰ ᠢᠭᠤᠯ ᠵᠢᠨ D. ᠢᠷ ᠮᠡᠭᠳᠦ ᠪᠠᠭ ᠠᠨ ᠠ 2. ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ ᠂ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠲᠡᠭᠡᠷ ᠠ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤ ᠭ ᠨᠢ ( ) A. B. C. D. 3. ᠵᠢᠷ ᠤᠭ ᠮᠡᠳᠤ ᠂ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠤᠣ ᠯ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠨᠢ ( ) A. B. C. D. 4. ᠨᠢᠭᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠨᠢ ᠵᠢᠷ ᠤᠭ ᠮᠡᠳᠤ ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢ ᠢ ᠦᠷ ᠦᠬᠦ ᠳ᠋ᠦ ᠪᠠᠡ ( ) ᠵᠢᠵᠢᠭ ᠲᠡᠭ ᠰᠢ ᠲ ᠦ᠋ᠷᠪᠠ ᠯᠵᠢᠨ ᠪᠡᠶ ᠡ ᠭᠡᠷ ᠡᠭᠰᠡᠨ ᠡ ᠃ A. 3 B. 4 C. 5 D. 6 5. ᠵᠢᠷᠤᠭ ᠲᠠᠬ ᠢ ᠪᠡᠶ ᠡ ᠢ ᠢᠨ ᠭᠤᠣ ᠯ ᠬ ᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷ ᠤᠭ ᠨᠢ ( ) A. B. C. D. 6. ᠵᠢᠷᠤᠭ ᠲᠠᠬᠢ ᠪᠣᠯ ᠲᠡᠭᠡᠷ ᠠ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠲᠦ ᠡᠯ ᠡ ᠪᠠᠶᠢᠷ ᠢ ᠲᠡ ᠭᠡᠷ ᠠ ᠲᠠᠯᠪᠢᠠᠠ ᠳᠠᠠᠠᠰᠡᠨ ᠵᠢᠵᠢᠭ ᠲᠡᠭᠰᠢ ᠲᠦ᠋ ᠷᠪᠠᠯ ᠵᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠲᠣᠭ ᠠ ᠢᠢ ᠲᠡ ᠮᠲᠡᠭᠯᠡ ᠵᠦ ᠲᠡᠯᠪ ᠢᠭᠰᠡᠨ ᠪᠠᠶᠢᠨ ᠠ ᠂ ᠲᠡ ᠭᠡᠪᠡᠯ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠤᠣ ᠯ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠨᠢ ( ) A. B. C. D. 7. ᠵᠢᠷ ᠤᠭ 2 ᠮᠡᠲᠤ ᠂ ᠶᠡᠭᠡ ᠪᠠᠭ ᠠ ᠨᠢ ᠠᠳᠠ ᠯᠢ ᠡᠳᠤᠢ ᠲᠡ ᠳᠤᠢ ᠵᠢᠵᠢᠭ ᠲᠡ ᠭᠰᠢ ᠲᠦ᠋ᠷᠪ ᠠᠯᠵᠢᠨ ᠪᠡᠶ ᠡ ᠪ ᠡᠷ ᠪ ᠦᠷᠢ ᠯᠳᠦᠭ ᠰᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠣ ᠣᠯ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠪᠠ ᠲᠡᠭᠡᠷ ᠠ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠪᠤᠯ ᠤᠨ ᠠ ᠃ ᠲ ᠡᠭᠡᠪᠠᠯ ᠲᠤᠰ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢ ᠪᠦᠷᠢᠯᠳᠦᠯᠦ ᠭᠰᠡᠡ ᠵᠢᠵᠢᠭ ᠲᠡᠭᠰᠢ ᠲᠦ᠋ᠷᠪ ᠠᠯᠵᠢ ᠨ ᠪ ᠡᠶ ᠡ ᠨᠢ ᠬᠠᠮᠤᠭ ᠤ ᠯᠠᠠ ᠳ᠋ᠤ ᠪᠠᠡ ( ) ᠭᠡᠰᠡᠭ ᠪᠡᠶᠢᠨ ᠡ ᠃ A. 13 B. 12 C. 11 D. 10 z 3 1 1 2 2 4 ᠵᠡᠭᠦ ᠨ ᠳᠡᠭᠡᠷ ᠡ ᠭᠣᠣᠯ (1) 俯视图左视图主视图 ᠳᠡᠭᠡᠷ ᠡ 俯视图左视图主视图 ᠭᠣᠣᠯ 俯视图左视图主视图 ᠵᠡᠭ ᠦᠨ ᠳᠡᠭᠡᠷ ᠡ ᠵᠡᠭ ᠦᠨ (2) 8. ᠵᠢᠷᠤᠭ ᠮᠡᠳᠤ ᠂ ᠰᠢᠷ ᠡᠭᠡᠨ ᠲᠡᠭᠡᠷ ᠠ ᠲ ᠡᠯᠪᠢᠠᠠ ᠰᠡᠡ ᠨᠢᠭᠡ ᠠᠶᠠᠭ ᠠᠨ ᠤ ᠲᠡᠭᠡᠷ ᠠ ᠬ ᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷ ᠤᠭ ᠨᠢ ( ) A. B. C. D. 9. ᠲᠤᠤᠷᠠ ᠬᠢ ᠵᠢᠷ ᠤᠭ ᠦ ᠳ ᠡ ᠴᠠ ᠲᠡᠭᠰᠢ ᠲᠦ᠋ᠷᠪ ᠠᠯᠵᠢ ᠨ ᠪ ᠡᠶ ᠡ ᠢᠢᠨ ᠲᠡᠯ ᠭᠡᠮᠠᠯ ᠵᠢᠷᠤ ᠭ ᠪᠣᠯᠬᠤ ᠨᠢ ( ) A. B. C . D. 10. ᠵᠢᠷᠤᠭ 3 ᠮᠡ ᠳᠤ ᠂ ᠨᠢ ᠭᠡ ᠴᠠᠬᠢᠯ ᠭᠠᠨ ᠪᠠᠭᠠᠨ ᠠ AB ᠰᠡᠬ ᠦᠳᠡᠷ ᠨᠢ ᠭᠠᠵᠠᠷ ᠦᠨ ᠭᠠᠳᠠ ᠷᠭᠤ ᠲᠡᠭᠡᠷ ᠠ ᠪ ᠠ ᠨᠢ ᠭᠡ ᠭᠡᠰᠡᠭ ᠨᠢ ᠬᠡᠷᠡᠮ ᠲᠡᠭᠡᠷ ᠠ ᠲᠤᠰᠪ ᠠ ᠃ ᠠᠳᠠᠯᠢ ᠴᠠᠭ ᠲᠦ ᠴᠡᠴᠡᠭ 1m ᠪᠣᠯᠬᠤ ᠮᠤᠳᠤᠨ ᠰᠢᠳᠠ ᠮ ᠢ ᠬᠠᠵᠠᠭᠤ ᠳ᠋ᠤᠨᠢ ᠪᠤᠰ ᠬᠠᠵᠤ ᠲᠠᠯᠪᠢᠪ ᠠ᠃ ᠲᠡᠬᠦ ᠨ ᠦ ᠰᠡᠬᠦᠳᠡ ᠷ ᠦᠨ ᠤᠷᠳᠤ ᠨᠢ 0.5m ᠂ ᠡᠨ ᠡ ᠦᠶ ᠠᠰ AB ᠢᠢᠨ ᠭᠠᠵᠠᠷ ᠲᠡᠭᠡᠷ ᠡᠬᠢ ᠰᠡᠬᠦᠳᠡ ᠷ BD ᠦᠨ ᠤᠷᠳᠤ ᠨᠢ 3m ᠂ ᠬᠡ ᠷᠡᠮ ᠲᠡᠭᠡᠷ ᠠ ᠲᠤᠰ ᠤᠭᠰ ᠠᠠ ᠰ ᠡᠬᠦᠳᠡ ᠷ CD ᠢᠢᠨ ᠤᠷᠳ ᠤ ᠨᠢ 2m ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠴᠠᠬ ᠢᠯᠭᠠᠨ ᠪᠠᠭᠠᠨ ᠠ AB ᠢᠢᠨ ᠦᠠᠳᠤᠷ ᠨᠢ ( ) A. 5𝑚 B. 6𝑚 C. 7𝑚 D. 8𝑚 ᠬᠣᠶ ᠠᠷ᠂ ᠬᠠᠭ ᠠᠯᠲᠠ ᠳ᠋ᠤ ᠲᠠᠭᠯ ᠠᠬᠤ ᠰᠡᠲᠤᠪ ᠃ ︵ᠰᠡᠲᠤᠪ ᠪᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲ ᠡ 2 4 ᠬᠤᠪᠢ ︶ 11. ᠨᠢᠭᠡᠨ ᠰᠤᠷᠤᠭᠴᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠦᠠᠳᠦ ᠷ ᠨᠢ 1. 4m ᠂ ᠶᠠᠮᠠᠷ ᠨᠢᠭᠡᠨ ᠴᠠᠭ ᠮᠦ᠋ᠴᠠ ᠳ᠋ᠤ ᠲᠡᠬᠦ ᠨ ᠦ ᠨᠠᠷᠠᠨ ᠤ ᠭᠡᠷᠡᠯ ᠲᠤᠤᠷᠠ ᠬᠢ ᠰ ᠡᠬᠦᠳᠡ ᠷ ᠨᠢ 1. 2m ᠂ ᠲᠡ ᠬᠦᠡ ᠲᠡᠢ ᠵᠡᠷᠭᠡᠯ ᠡᠳᠡᠭᠡ ᠪᠡᠶ ᠢᠭ ᠠ ᠨᠢᠭᠡ ᠰᠠᠭ ᠤᠷᠢ ᠮᠤᠳᠤᠨ ᠤ ᠰ ᠡᠬᠦᠳᠡ ᠷ ᠨᠢ 3.6m ᠪᠡᠶᠢᠵᠡᠢ ᠂ ᠲᠡᠭᠡᠪ ᠠᠯ ᠲᠤᠰ ᠮᠤᠳᠤᠨ ᠤ ᠦᠠᠳᠤᠷ ᠨᠢ ( ) m 12. ᠨᠢᠭᠡᠨ ᠤᠷᠳᠤ ᠲᠦ᠋ ᠷᠪᠠᠯ ᠵᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠣᠣ ᠯ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ᠂ ᠵᠡᠬᠦᠨ ᠬᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷ ᠤᠭ ᠵᠢᠴᠢ ᠬᠠᠷᠠᠭ ᠠᠯᠵᠠᠭᠰᠠᠠ ᠲᠣᠭ ᠠ ᠪᠠᠷ ᠢᠮᠳᠡ ᠨᠢ ᠵᠢᠷᠤᠭ 4 ᠮᠡ ᠳᠤ (ᠨᠢᠭᠡᠴᠢ ᠨᠢ cm )᠂ ᠲᠡᠭᠡᠪ ᠠᠯ ᠲᠡ ᠬᠦᠨ ᠦ ᠲᠡᠭᠡᠷ ᠠ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠦᠨ ᠲᠠᠯᠠᠪ ᠠᠢ ᠨᠢ ( ) cm 2 13 . ᠵᠢᠷ ᠤᠭ 5 ᠮᠡ ᠳᠤ ᠂ ᠨᠢᠭᠡ ᠴᠠᠬᠢᠯ ᠭᠠᠨ ᠪᠠᠭᠠᠨ ᠠ ᠢᠢᠨ A B ᠭᠡᠰᠡᠭ ᠨᠢ ᠨᠡᠷᠡᠡ ᠦ ᠭᠡᠷᠡᠯ ᠲᠤᠤᠷᠠ ᠬᠢ ᠰ ᠡᠬᠦᠳᠡ ᠷ CD ᠢᠢᠨ ᠤᠷᠳᠤ ᠨᠢ 1.2m ᠂ ᠨᠠ ᠷᠠᠠ ᠤ ᠭᠡᠷᠡᠯ ᠪᠠ ᠭᠠᠵᠠᠷ ᠦᠨ ᠲᠦ᠋ᠪᠰᠢᠨ ᠦ ᠬᠠᠪᠴ ᠢᠭᠰᠠᠠ ᠦᠠᠴᠦ ᠭ ᠨᠢ ∠A CD ＝60° ᠂ ᠲᠡᠭᠡᠪ ᠠᠯ AB ᠢᠢᠨ ᠤᠷ ᠳᠤ ᠨᠢ ( ) m 14. ᠲᠠ ᠷᠠᠭᠠᠬ ᠢ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠢ ᠦᠠᠳᠤᠰᠤ ᠯᠠᠪᠠᠯ ᠲᠤᠰ ᠭᠧᠣᠮᠧᠲ᠋ ᠷᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠨᠢ ( ) ᠵᠢᠵ ᠢᠭ ᠲᠡ ᠭᠰᠢ ᠲᠦ᠋ ᠷᠪᠠᠯ ᠵᠢᠨ ᠪᠡᠶ ᠡ ᠪᠠᠷ ᠪᠦᠷᠢ ᠯᠳᠦᠭ ᠰᠡᠨ ᠪᠠᠶᠢᠨ ᠠ ᠃ 15. ᠴᠡ ᠴᠡᠭ ᠪᠠ ᠰᠡᠴᠡᠠ ᠬᠤᠶ ᠠᠷ ᠨᠡᠷᠡᠡ ᠤ ᠭᠡᠷᠡᠯ ᠲᠤᠤᠷ ᠠ ᠠ ᠯᠬᠤᠵ ᠤ ᠪ ᠤᠢ᠂ ᠴᠡᠴᠡᠭ ᠦᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠦᠠᠳᠦ ᠷ ᠨᠢ 1.75 m ᠪᠡᠶᠢᠵᠤ ᠲᠡᠬᠦ ᠨ ᠦ ᠰᠡᠬᠦᠳᠡ ᠷ ᠦᠨ ᠤᠷᠳᠤ ᠨᠢ 2.0m ᠂ ᠰ ᠡᠴᠡᠠ ᠤ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠦᠠᠳᠤᠷ ᠨᠢ ᠴᠡ ᠴᠡᠭ ᠡᠴᠠ 5cm ᠪᠤᠭᠤᠨᠢ ᠂ ᠡᠨ ᠡ ᠦ ᠶᠡᠰ ᠰᠡᠴᠡᠠ ᠤ ᠰ ᠡᠬᠦᠳᠡ ᠷ ᠦᠨ ᠤᠷᠳᠤ ᠨᠢ ( )m 16. ᠵᠢᠷ ᠤᠭ 6 ᠮᠡ ᠳᠤ ᠂ ᠬᠡᠷ ᠡᠮ D ᠳᠡᠭᠡᠷ ᠠ ᠨᠢ ᠭᠡ ᠳ᠋ᠧᠩ ᠪᠤᠢ ᠂ ᠪ ᠠᠲᠤ A ᠭᠠᠵᠠᠷ ᠵᠤᠭᠰᠤ ᠬᠤ ᠳ᠋ᠤ ᠲᠡᠬᠦ ᠨ ᠦ ᠰᠡᠬᠦᠳᠡ ᠷ ᠢᠢ ᠨ ᠤᠷ ᠳᠤ ᠪᠠ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠤᠷ ᠳᠤ ᠨᠢ ᠪ ᠦᠷ 1.6m ᠂ ᠪ ᠠᠲᠤ ᠬᠡᠷᠡᠮ 3 2 4 4 (3) ᠭᠣᠣᠯ ᠵᠡᠭᠦ ᠨ (4) ᠭᠣᠣᠯ ᠵᠡᠭ ᠦᠨ ᠳᠡᠭᠡᠷ ᠡ ᠵᠦ᠋ᠭ 1m ᠶᠠᠪᠤ ᠭᠠᠳ ᠴᠡ ᠭ B ᠬᠦᠷᠬᠦ ᠦᠶ ᠡᠰ ᠲᠡᠬᠦ ᠨ ᠦ ᠰᠡᠬᠦᠳᠡ ᠷ ᠨᠢ ᠶᠠᠭ ᠰᠡᠶᠢᠬ ᠠᠨ ᠴᠡ ᠭ A ᠲᠡᠭᠡᠷ ᠠ ᠲᠤᠰᠪᠠ᠃ ᠲᠡᠭᠡᠪ ᠠᠯ CD ＝( ) 17. ᠵᠢᠷ ᠤᠭ ᠮᠡᠳᠤ ᠂ ᠪᠡᠶ ᠡ ᠢ ᠢᠨ ᠦᠠ ᠳᠤᠷ ᠨᠢ 1.6m ᠪᠣᠯᠬᠤ ᠰᠤᠷᠤᠭᠴᠢ ᠨᠢᠭᠡᠨ ᠰᠠᠭ ᠤᠷᠢ ᠮᠣᠳᠣ ᠨ ᠤ ᠦᠠᠳᠦ ᠷ ᠢ ᠭᠡᠮᠵᠢᠬᠦ ᠢᠢᠨ ᠲᠦ᠋ ᠯᠦᠭᠡ ᠂ ᠮᠤᠳᠤᠨ ᠤ ᠰ ᠡᠬᠦᠳᠡ ᠷ BA ᠢᠢᠨ ᠲᠠᠭ ᠤ B ᠡᠴᠠ A ᠲᠡᠶᠢᠰ ᠢ ᠠ ᠯᠬᠤᠪᠠ ᠂ ᠴᠡᠭ C ᠬᠦᠷ ᠬᠦ ᠦᠶ ᠡᠰ ᠂ ᠲᠡᠬ ᠦᠨ ᠦ ᠰ ᠡᠬᠦᠳᠡ ᠷ ᠦ ᠨ ᠤᠷ ᠤᠢ ᠦ ᠨ ᠴᠡ ᠭ ᠨᠢ ᠶᠠᠭ ᠰᠠᠶᠢᠬ ᠠᠨ ᠮᠤᠳᠤᠨ ᠤ ᠰᠡᠬ ᠦᠳᠡᠷ ᠦ ᠨ ᠤᠷ ᠤᠢ ᠢᠢᠨ ᠴᠡᠭ ᠲᠡᠢ ᠲᠠᠪᠬᠤ ᠴᠠᠵᠡᠢ ᠃ ᠭᠡᠮᠵᠢᠭᠡᠳ ᠤ ᠯᠤᠭᠰ ᠠᠠ ᠨᠢ BC = 3.2m , CA = 0.8m ᠂ ᠲᠡᠭᠡᠪ ᠠᠯ ᠮᠤᠳᠤᠨ ᠤ ᠦᠠᠳᠤᠷ ᠨᠢ 18. ᠵᠢᠷ ᠭᠠᠯ ᠦ ᠨ ᠪ ᠡᠶ ᠡ ᠢᠢᠨ ᠦᠠᠳᠤᠷ ᠨᠢ 1.7m ᠂ ᠲᠡ ᠬᠦᠨ ᠦ ᠨᠠᠷ ᠠᠨ ᠤ ᠭᠡᠷᠡᠯ ᠲᠤᠤᠷᠠ ᠬᠢ ᠰ ᠡᠬᠦᠳᠡ ᠷ ᠦᠨ ᠤᠷᠳᠤ ᠨᠢ 0.85m ᠪᠣᠯᠬᠤ ᠢᠢ ᠭᠡᠮᠵᠢᠨ ᠣᠯ ᠪᠠ ᠂ ᠲᠡ ᠷᠡ ᠬᠤᠶ ᠠᠷ ᠭᠠᠷ ᠢᠢᠠᠨ ᠠᠰ ᠲᠡᠭᠡᠭᠰ ᠢ ᠡᠷ ᠬᠦᠭᠰᠡᠡ ᠳ᠋ᠦ ᠰᠡᠬᠦᠳᠡ ᠷ ᠦᠨ ᠤᠷ ᠳᠤ ᠨᠢ 1 .1m ᠪᠣ ᠯᠪᠠ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠵᠢᠷ ᠭᠠᠯ ᠦ ᠨ ᠠ ᠰ ᠲᠡ ᠭᠡᠭᠰᠢ ᠡᠷ ᠬᠦᠭᠰᠡᠡ ᠭᠠᠷ ᠨᠢ ᠲᠤᠯ ᠤᠭᠠᠢ ᠢᠢᠨ ᠭᠡᠰᠡᠭ ᠡᠴᠠ ( ) m ᠲᠡᠭᠡ ᠭᠰᠢ ᠪᠠᠶᠢᠨ ᠠ ᠃ ᠭᠤᠷᠪ ᠠ᠂ ᠪᠣᠳᠣᠵ ᠤ ᠬᠠᠷ ᠢᠭᠤᠯ ᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ ︵ ᠨᠠᠢᠲᠡ 66 ᠬᠤᠪᠢ ︶ 19. (8 ᠬᠤᠪᠢ ) ᠲᠠ ᠷᠠᠭᠠᠬ ᠢ ᠵᠢᠷ ᠤᠭ ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷᠤᠭ ᠪᠤᠯ ᠤᠨ ᠠ ᠃ ᠲᠡ ᠭᠡᠪᠠᠯ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠨᠢ ᠶᠠᠮᠠ ᠷ ᠪᠡ ᠶ ᠡ ᠪ ᠣᠯᠬᠤ ᠪᠤᠢ︖ ᠪᠠᠰᠠ ᠲᠡᠬᠦ ᠨ ᠦ ᠡᠵᠡᠯ ᠡᠬᠦᠨ ᠢ ᠨᠢ ᠣᠯ ᠃ 20. ( 8 ᠬᠤᠪᠢ ) ᠲᠠ ᠷᠠᠭᠠᠬ ᠢ ᠵᠢᠷ ᠤᠭ ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢ ᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷᠠᠭ ᠠᠨ ᠵᠢᠷᠤᠭ ᠪᠤᠯᠤᠨ ᠠ ᠃ ᠲᠡ ᠭᠡᠪᠠᠯ ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠨᠢ ᠶᠠᠮᠠ ᠷ ᠪᠡᠶ ᠡ ᠪ ᠣᠯᠬᠤ ᠪᠤᠢ ︖ ᠪᠠᠰᠠ ᠲᠡᠬᠦ ᠨ ᠦ ᠵᠢᠷᠤᠭ ᠢ ᠵᠢᠷᠤᠵ ᠤ ᠭᠠᠷ ᠭ ᠠ ᠃ 21. (1 0 ᠬ ᠤᠪᠢ ) ᠲᠠ ᠷᠠᠭᠠᠬ ᠢ ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠲᠤᠨᠤᠭ ᠦᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠮᠦ᠋ᠨ ᠂ ᠲᠤᠰ ᠲᠤᠨᠤᠭ ᠦᠨ ᠭᠠᠳᠠ ᠷᠭᠤ ᠢᠢᠨ ᠲᠠᠯᠠᠪ ᠠᠢ ᠢᠢ ᠣᠯ ᠃ (6) (7) ᠳᠡᠭᠡᠷ ᠡ ᠭᠣᠣᠯ ᠵᠡᠭᠦ ᠨ ᠭᠣᠣᠯ ᠵᠡᠭᠦ ᠨ ᠳᠡᠭᠡᠷ ᠡ ᠭᠣᠣᠯ ᠳᠡᠭᠡᠷ ᠡ ᠵᠡᠭᠦ ᠨ 22. (1 0 ᠬᠤᠪᠢ ) ᠲᠠ ᠷᠠᠭᠠᠬ ᠢ ᠵᠢᠷ ᠤᠭ ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠲᠡ ᠯᠭᠡᠮᠠ ᠯ ᠵᠢᠷ ᠤᠭ ᠪᠤᠯᠤᠨ ᠠ ᠃ (1) ᠡᠨ ᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠨ ᠢ ᠶᠠᠮᠠ ᠷ ᠪᠡ ᠶ ᠡ ᠪ ᠣᠯᠬᠤ ᠪᠤ ᠢ ︖ (2) ᠡᠨᠡ ᠭᠧᠣᠮᠧᠲ᠋ᠷ ᠢ ᠢᠢᠨ ᠪᠡᠶ ᠡ ᠢᠢ ᠨ ᠭᠤᠷᠪ ᠠᠨ ᠬᠠᠷ ᠠᠭᠠᠨ ᠵᠢᠷᠤᠭ ᠢ ᠵᠢᠷᠤ ᠃ (3) ᠲᠡᠬᠦ ᠨ ᠦ ᠡᠵᠡᠯᠡᠬᠦ ᠨ ᠢ ᠣᠯ ᠃ 23. ( 1 0 ᠬ ᠤᠪᠢ ) (1) ᠨᠢᠭᠡ ᠮᠤᠳᠤ ᠨ ᠪ ᠠᠭᠠᠨ ᠠ ᠢᠢ ᠵᠢᠷ ᠤᠭ 1ᠮᠡ ᠳᠤ ᠪ ᠠᠷ ᠭᠠᠵᠠᠷ ᠲᠡᠭᠡᠷ ᠠ ᠪᠤ ᠰᠬᠠᠵ ᠤ ᠲᠠ ᠯᠪᠢᠪ ᠠ ᠂ ᠵᠢᠷ ᠤᠭ ᠲᠡᠭᠡᠷ ᠠ ᠲᠡ ᠬᠦᠨ ᠦ ᠨᠠ ᠷᠠᠨ ᠤ ᠭᠡᠷ ᠠᠯ ᠲᠤ ᠤᠷᠠᠬ ᠢ ᠰ ᠡᠭᠦᠳᠡ ᠷ ᠢ ᠵᠢᠷᠤ ᠃ ( ᠭᠡᠷᠴᠢᠮ CD ᠪᠠᠷ ᠢᠯ ᠡᠷᠭᠡᠶᠢᠯ ᠨ ) ᠃ (2) ᠵᠢᠷ ᠤᠭ 2 ᠨᠢ ᠬᠤᠶ ᠠᠷ ᠲᠡ ᠮᠳᠡᠭᠲᠦ ᠪᠠᠭ ᠠᠨ ᠠ ᠵᠢᠴᠢ ᠲᠡᠬᠦ ᠨ ᠦ ᠨᠠᠷᠠᠠ ᠤ ᠭᠡᠷ ᠡᠯ ᠲᠤᠤᠷᠠ ᠬᠢ ᠰ ᠡᠬᠦᠳᠡ ᠷ ᠪᠤᠯᠤᠨ ᠠ ᠂ ᠵᠢᠷᠤᠭ ᠲᠡᠭᠡᠷ ᠠ ᠭᠡᠷ ᠡᠯ ᠡᠬ ᠦᠰᠭᠡᠭ ᠴᠢ ᠢᠢᠨ ᠪᠠᠶᠢᠷ ᠢ ( ᠴᠡᠭ P ᠪᠠᠷ ᠢᠯᠡᠷ ᠭᠡᠶᠢᠯᠨ ) ᠢ ᠵᠢᠷᠤᠵ ᠤ ᠂ ᠪᠠᠰᠠ ᠵᠢᠷᠤᠭ ᠲᠠᠬᠢ ᠬᠦᠮᠤᠨ ᠤ ᠭᠡᠷᠡᠯ ᠡᠬᠦᠰᠭᠡ ᠭᠴᠢ p ᠲᠤᠤᠷᠠ ᠬᠢ ᠰᠡᠬᠦᠳᠡ ᠷ ( ᠭᠡᠷ ᠴᠢᠮ EF ᠢᠢᠡᠷ ᠢᠯ ᠡᠷᠭᠡᠶᠢᠯ ᠨ ) ᠢ ᠵᠢᠷᠤ ᠃ ᠨᠠᠷᠠᠨ ᠤ ᠭᠡᠷᠡᠯ ᠮᠤᠳᠤᠨ ᠪᠠᠭᠠᠨ ᠠ A B 20 10