Stream on BOBR: https://bobr.video/watch?v=4d41bc98-a... Materials for the web: https://1.shkolkovo.online/public-sto... 🥇Six-month course of preparation for the Unified State Exam/Basic State Exam ⬇️ Unified State Exam: https://3.shkolkovo.online/na-poryado... Basic State Exam: https://3.shkolkovo.online/na-poryado... 10th grade: https://3.shkolkovo.online/na-poryado... Shkolkovo promotions and discounts👉🏻 https://3.shkolkovo.online/special?ut... 📲TG channel on mathematics with MO👉🏻 https://t.me/MO_EGE 📲VK group👉🏻 https://vk.com/shkolkovo_math Mailing list of useful VK materials 👉🏻 https://vk.com/app5898182_-185634090#... Our YouTube channels: Preparation for the 2025 Unified State Exam in Shkolkovo ✔️ Mathematics with MO and Russian language with TA (Shkolkovo's main channel): / @shkolkovo ✔️ Maxim Koval. Vlog of a math teacher: / @kovalmo ✔️ Physics with AB: / @shkolkovo_phys ✔️ Biology with EB: / @shkolkovo_bio ✔️ Chemistry Mutagen: / @mutagenege ✔️ Social Science and History Histructor: / @histructor ✔️ History with AB: / @shkolkovo_history ✔️ English language: / @shkolkovo_english ✔️ Computer Science BU: / @infbu ✔️ Babaev Alipasha Expert of the Unified State Exam in Mathematics: / @egemath_expert Preparation for the 2025 OGE in Shkolkovo ✔️ Mathematics with AF and Russian language with CN (Preparation for the OGE): / @shkolkovo-oge ✔️ Biology OGE with EB: / @shkolkovo_bio ✔️ Physics OGE with GK: / @shkolkovogk ✔️ Social Science OGE with EK: / @kant_soc ✔️ Computer Science OGE with MS: / @shkolkovo_inf_oge Olympiad areas in Shkolkovo ✔️ Economics. Shkolkovo Olympiads: / @econbyshkolkovo ✔️ Olympiad Mathematics with DA: / @shkolkovo_olymp ✔️ Olympiad Physics with AB / @shkolkovo_phys 00:00 Hello everyone! MO plan for 4-hour webinars 03:23 Is it possible to study only #3 (without #14)? How are we going to work today? Block 1: Parallelepiped Problems 06:17 #1. Rectangular parallelepiped: definition and basic properties. Spatial Pythagorean theorem. Diagonal of a parallelepiped 14:07 #2. Volume and surface area of ​​a parallelepiped. Cube and its properties. Angle between lines in space. Angle between intersecting lines in a cube 27:05 #3. Sine of the angle between intersecting lines in a cube 31:32 #4. Pyramid and regular pyramid. Volume of a pyramid. Area of ​​a right triangle. Volume of a triangular pyramid 40:30 #5. Volume of a quadrangular pyramid 42:36 #6. Prism and its volume 52:57 #7. Volume of a triangular prism cut off from a cube 01:01:53 #8. The method of multipliers for finding the volume of the second polyhedron given the volume of the first. We apply it to parallelepipeds Block 2: Problems about a prism 01:06:29 #9. Area of ​​the lateral surface of a cut off prism 01:15:13 #10. Formula for the volume of an arbitrary prism. The volume of the original prism by the volume of the cut off prism 01:19:32 #11. The regular prism. The volume of the cut off prism 01:23:22 #12. The volume of a triangular pyramid in a regular prism 01:26:50 #13. Euclid's spatial rails! We transform one pyramid into another to find the volume of the desired one 01:34:55 The dog stole MO's shorts Block 3: Problems about the pyramid 01:37:08 #14. The regular pyramid - basic properties. The diagonal of a square at the base from the height and the lateral edge 01:43:43 #15. The volume of the cut off pyramid through the relationship of the areas of the bases and heights 01:46:08 #16. Volume of a regular 4-sided pyramid with known edges 01:51:48 #17. Multiplier method for the volume of a cut-off pyramid 01:55:00 #18. Volume of a pyramid inscribed in a cube Block 4: Problems about solids of revolution (cylinder, cone, sphere) 01:58:48 #19. Cylinder - all the facts and formulas at once! Lateral surface area 02:04:11 #20. Multiplier method for the volume of the second cylinder 02:09:25 A method for those who did not understand the multiplier method 02:12:47 #21. Cone - all the formulas. Length of the generatrix 02:18:31 #22. And again the multiplier method 02:21:38 #23. Spatial similarity! Cone-shaped vessel with water, multiplier method 02:33:40 #24. Ratio of cone generators from known ratios 02:42:20 #25. Ball! Area of ​​a circle from surface area 02:44:44 #26, 27. The similarity of balls kills the problem! Block 5: Inscribed problems 02:49:04 #28. A ball is inscribed in a cube. Surface area of ​​a sphere 02:53:09 #29. Volume of a cube from volume of a sphere 02:56:12 #30. A cone is inscribed in a cylinder. Volume of a cylinder 02:58:40 #31. Lateral surface area of ​​a cone 03:06:13 #32. A ball is inscribed in a cylinder. Surface area of ​​a sphere 03:10:32 #33. Volume of the sphere 03:13:32 #34. The cone is inscribed in the sphere. Volume of the sphere 03:17:08 #35. Length of the generatrix 03:19:17 That's it, the last task is killed! Results of the web and go go in Russian