B\u00e0i 1 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O b\u00e1n k\u00ednh r n\u1eb1m tr\u00ean m\u1eb7t ph\u1eb3ng (P). T\u1eeb nh\u1eefng \u0111i\u1ec3m M n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n n\u00e0y ta k\u1ebb nh\u1eefng \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi (P). Ch\u1ee9ng minh r\u1eb1ng nh\u1eefng \u0111\u01b0\u1eddng th\u1eb3ng nh\u01b0 v\u1eady n\u1eb1m tr\u00ean m\u1ed9t m\u1eb7t tr\u1ee5 tr\u00f2n xoay. H\u00e3y x\u00e1c \u0111\u1ecbnh tr\u1ee5c v\u00e0 b\u00e1n k\u00ednh c\u1ee7a m\u1eb7t tr\u1ee5 \u0111\u00f3.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-1-trang-39-sgk-hinh-hoc-12.png\")
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G\u1ecdi d l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (P) t\u1ea1i t\u00e2m O c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n (T).<\/p>\n
T\u1eeb \u0111i\u1ec3m M tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n (T), v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng \u0394 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (P).<\/p>\n
Khi \u0111\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng \u0394 song song v\u1edbi d v\u00e0 lu\u00f4n c\u00e1ch d m\u1ed9t kho\u1ea3ng b\u1eb1ng r.<\/p>\n
\u0110\u01b0\u1eddng th\u1eb3ng \u0394 thu\u1ed9c m\u1eb7t tr\u1ee5 tr\u00f2n xoay c\u00f3 tr\u1ee5c l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng d v\u00e0 b\u00e1n k\u00ednh r.<\/p>\n
B\u00e0i 2 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0Trong m\u1ed7i tr\u01b0\u1eddng h\u1ee3p sau \u0111\u00e2y, h\u00e3y g\u1ecdi t\u00ean c\u00e1c h\u00ecnh tr\u00f2n xoay ho\u1eb7c kh\u1ed1i tr\u00f2n xoay sinh ra b\u1edfi:<\/strong><\/span><\/p>\na) Ba c\u1ea1nh c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt khi quay quanh \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a c\u1ea1nh th\u1ee9 t\u01b0,<\/strong><\/span><\/p>\nb) Ba c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00e2n khi quay quanh tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a n\u00f3.<\/strong><\/span><\/p>\nc) M\u1ed9t tam gi\u00e1c vu\u00f4ng k\u1ec3 c\u1ea3 c\u00e1c \u0111i\u1ec3m trong c\u1ee7a tam gi\u00e1c vu\u00f4ng \u0111\u00f3 khi quay quanh \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng.<\/strong><\/span><\/p>\nd) M\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt k\u1ec3 c\u1ea3 c\u00e1c \u0111i\u1ec3m trong c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt \u0111\u00f3 khi quay quanh \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a m\u1ed9t c\u1ea1nh.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
a) Khi quay m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt xung quanh \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a m\u1ed9t c\u1ea1nh th\u00ec ta \u0111\u01b0\u1ee3c m\u1ed9t h\u00ecnh tr\u1ee5<\/p>\n
b) Khi quay m\u1ed9t tam gi\u00e1c c\u00e2n xung quanh tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a n\u00f3 ta \u0111\u01b0\u1ee3c m\u1ed9t h\u00ecnh n\u00f3n tr\u00f2n xoay<\/p>\n
c) M\u1ed9t tam gi\u00e1c vu\u00f4ng k\u1ec3 c\u1ea3 \u0111i\u1ec3m trong c\u1ee7a n\u00f3 khi quay xung quanh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng th\u00ec t\u1ea1o ra m\u1ed9t kh\u1ed1i n\u00f3n tr\u00f2n xuay.<\/p>\n
d) M\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt k\u1ec3 c\u1ea3 c\u00e1c \u0111i\u1ec3m trong c\u1ee7a n\u00f3 khi quay quanh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a m\u1ed9t c\u1ea1nh th\u00ec t\u1ea1o ra m\u1ed9t kh\u1ed1i tr\u1ee5 tr\u00f2n xoay.<\/p>\n
B\u00e0i 3 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0M\u1ed9t h\u00ecnh n\u00f3n c\u00f3 \u0111\u01b0\u1eddng cao h = 20cm, b\u00e1n k\u00ednh \u0111\u00e1y r = 25cm.<\/strong><\/span><\/p>\na)T\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh n\u00f3n \u0111\u00e3 cho.<\/strong><\/span><\/p>\nb)T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i n\u00f3n \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1edfi h\u00ecnh n\u00f3n \u0111\u00f3.<\/strong><\/span><\/p>\nc)M\u1ed9t thi\u1ebft di\u1ec7n \u0111i qua \u0111\u1ec9nh c\u1ee7a h\u00ecnh n\u00f3n v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m c\u1ee7a \u0111\u00e1y \u0111\u1ebfn m\u1eb7t ph\u1eb3ng thi\u1ebft di\u1ec7n l\u00e0 12cm. T\u00ednh di\u1ec7n t\u00edch thi\u1ebft di\u1ec7n \u0111\u00f3<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-3-trang-39-sgk-hinh-hoc-12.png\")
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-3-trang-39-sgk-hinh-hoc-12-1.png\")
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![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-3-trang-39-sgk-hinh-hoc-12-2.png\")
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B\u00e0i 4 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0Trong kh\u00f4ng gian cho hai \u0111i\u1ec3m A, B c\u1ed1 \u0111\u1ecbnh v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i AB = 20cm. G\u1ecdi d l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng thay \u0111\u1ed5i lu\u00f4n \u0111i qua A v\u00e0 c\u00e1ch B m\u1ed9t kho\u1ea3ng b\u1eb1ng 10cm. Ch\u1ee9ng t\u1ecf r\u1eb1ng \u0111\u01b0\u1eddng th\u1eb3ng d lu\u00f4n n\u1eb1m tr\u00ean m\u1ed9t m\u1eb7t n\u00f3n, h\u00e3y x\u00e1c \u0111\u1ecbnh m\u1eb7t n\u00f3n \u0111\u00f3 (tr\u1ee5c v\u00e0 g\u00f3c \u1edf \u0111\u1ec9nh).<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-4-trang-39-sgk-hinh-hoc-12.png\")
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T\u1eeb B v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi d v\u00e0 c\u1eaft d t\u1ea1i H.<\/p>\n
Ta c\u00f3 BH = 10cm = d(B,d)<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-4-trang-39-sgk-hinh-hoc-12-1.png\")
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V\u1eady \u0111\u01b0\u1eddng th\u1eb3ng d n\u1eb1m tr\u00ean m\u1eb7t n\u00f3n c\u00f3 \u0111\u1ec9nh l\u00e0 A, tr\u1ee5c l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 g\u00f3c \u1edf \u0111\u1ec9nh l\u00e0 2\u03b1 = 60o<\/sup><\/p>\n\n
B\u00e0i 5 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0M\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r = 5cm v\u00e0 c\u00f3 kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u00e1y b\u1eb1ng 7cm.<\/strong><\/span><\/p>\n\n
\u00a0<\/strong><\/span><\/p>\na)T\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh tr\u1ee5 v\u00e0 th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5 t\u1ea1o n\u00ean.<\/strong><\/span><\/p>\nb)C\u1eaft kh\u1ed1i tr\u1ee5 b\u1edfi m\u1ed9t m\u1eb7t ph\u1eb3ng song song v\u1edbi tr\u1ee5c v\u00e0 c\u00e1ch tr\u1ee5c 3cm. H\u00e3y t\u00ednh di\u1ec7n t\u00edch c\u1ee7a thi\u1ebft di\u1ec7n \u0111\u01b0\u1ee3c t\u1ea1o n\u00ean.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-5-trang-39-sgk-hinh-hoc-12.png\")
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\n
B\u00e0i 6 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0C\u1eaft m\u1ed9t h\u00ecnh n\u00f3n b\u1eb1ng m\u1ed9t m\u1eb7t ph\u1eb3ng qua tr\u1ee5c c\u1ee7a n\u00f3 ta \u0111\u01b0\u1ee3c thi\u1ebft di\u1ec7n l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh 2a. T\u00ednh di\u1ec7n t\u00edch xung quanh v\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n \u0111\u00f3.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-6-trang-39-sgk-hinh-hoc-12.png\")
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![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-6-trang-39-sgk-hinh-hoc-12-1.png\")
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B\u00e0i 7 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0M\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 b\u00e1n k\u00ednh r v\u00e0 chi\u1ec1u cao h = r \u221a3<\/strong><\/span><\/p>\na)T\u00ednh di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh tr\u1ee5.<\/strong><\/span><\/p>\nb)T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 t\u1ea1o n\u00ean b\u1edfi h\u00ecnh tr\u1ee5 \u0111\u00e3 cho.<\/strong><\/span><\/p>\nc)Cho hai \u0111i\u1ec3m A v\u00e0 B l\u1ea7n l\u01b0\u1ee3t n\u1eb1m tr\u00ean hai \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y sao cho g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 tr\u1ee5c c\u1ee7a h\u00ecnh tr\u1ee5 b\u1eb1ng 30o<\/sup>.T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 tr\u1ee5c c\u1ee7a h\u00ecnh tr\u1ee5.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-7-trang-39-sgk-hinh-hoc-12.png\")
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-7-trang-39-sgk-hinh-hoc-12-1.png\")
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B\u00e0i 8 (trang 40 SGK H\u00ecnh h\u1ecdc 12):\u00a0M\u1ed9t h\u00ecnh tr\u1ee5 c\u00f3 hai \u0111\u00e1y l\u00e0 hai h\u00ecnh tr\u00f2n (O; r) v\u00e0 (O‘<\/sup>;r). Kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111\u00e1y l\u00e0 OO’ = r . M\u1ed9t h\u00ecnh n\u00f3n c\u00f3 \u0111\u1ec9nh l\u00e0 O’ v\u00e0 c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh tr\u00f2n (O;r).<\/strong><\/span><\/p>\n\n
a)G\u1ecdi S1<\/sub>\u00a0l\u00e0 di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh tr\u1ee5 v\u00e0 S2<\/sub>\u00a0l\u00e0 di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh n\u00f3n, h\u00e3y t\u00ednh t\u1ec9 s\u1ed1 S1<\/sub>\/S2<\/sub>\u00a0.<\/strong><\/span><\/p>\nb)M\u1eb7t xung quanh c\u1ee7a h\u00ecnh n\u00f3n chia kh\u1ed1i tr\u1ee5 th\u00e0nh hai ph\u1ea7n, h\u00e3y t\u00ednh t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch hai ph\u1ea7n \u0111\u00f3.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-8-trang-40-sgk-hinh-hoc-12.png\")
<\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-8-trang-40-sgk-hinh-hoc-12-1.png\")
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-8-trang-40-sgk-hinh-hoc-12-2.png\")
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B\u00e0i 9 (trang 40 SGK H\u00ecnh h\u1ecdc 12):\u00a0C\u1eaft h\u00ecnh n\u00f3n \u0111\u1ec9nh S b\u1edfi m\u1eb7t ph\u1eb3ng \u0111i qua tr\u1ee5c ta \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c vu\u00f4ng c\u00e2n c\u00f3 c\u1ea1nh huy\u1ec1n b\u1eb1ng a \u221a2<\/strong><\/span><\/p>\na)T\u00ednh di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i n\u00f3n t\u01b0\u01a1ng \u1ee9ng.<\/strong><\/span><\/p>\nb)Cho d\u00e2y cung BC c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y h\u00ecnh n\u00f3n sao cho m\u1eb7t ph\u1eb3ng (SBC) t\u1ea1o v\u1edbi m\u1eb7t ph\u1eb3ng ch\u1ee9a \u0111\u00e1y h\u00ecnh n\u00f3n g\u00f3c 60o<\/sup>.T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c SBC.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-9-trang-40-sgk-hinh-hoc-12.png\")
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![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-9-trang-40-sgk-hinh-hoc-12-1.png\")
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-9-trang-40-sgk-hinh-hoc-12-2.png\")
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B\u00e0i 10 (trang 40 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh tr\u1ee5 c\u00f3 b\u00e1n k\u00ednh r v\u00e0 c\u00f3 chi\u1ec1u cao c\u0169ng b\u1eb1ng r. H\u00ecnh vu\u00f4ng ABCD c\u00f3 hai c\u1ea1nh AB v\u00e0 CD l\u1ea7n l\u01b0\u1ee3t l\u00e0 c\u00e1c d\u00e2y cung c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y, c\u00f2n c\u1ea1nh BC v\u00e0 AD kh\u00f4ng ph\u1ea3i l\u00e0 \u0111\u01b0\u1eddng sinh c\u1ee7a h\u00ecnh tr\u1ee5. T\u00ednh di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh vu\u00f4ng \u0111\u00f3 v\u00e0 c\u00f4sin c\u1ee7a g\u00f3c gi\u1eefa m\u1eb7t ph\u1eb3ng ch\u1ee9a h\u00ecnh vu\u00f4ng v\u00e0 m\u1eb7t ph\u1eb3ng \u0111\u00e1y.<\/strong><\/span><\/p>\nL\u1eddi gi\u1ea3i:<\/b><\/p>\n
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-10-trang-40-sgk-hinh-hoc-12-1.png\")
![\"\"](\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/bai-10-trang-40-sgk-hinh-hoc-12-2.png\")
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<\/p>\n","protected":false},"excerpt":{"rendered":"
B\u00e0i 1 (trang 39 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O b\u00e1n k\u00ednh r n\u1eb1m tr\u00ean m\u1eb7t ph\u1eb3ng (P). T\u1eeb nh\u1eefng \u0111i\u1ec3m M n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n n\u00e0y ta k\u1ebb nh\u1eefng \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi (P). Ch\u1ee9ng minh r\u1eb1ng nh\u1eefng \u0111\u01b0\u1eddng th\u1eb3ng nh\u01b0 v\u1eady n\u1eb1m tr\u00ean m\u1ed9t m\u1eb7t tr\u1ee5 tr\u00f2n xoay. H\u00e3y x\u00e1c […]<\/p>\n","protected":false},"author":3,"featured_media":20573,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1298],"tags":[1377,1356,1376],"yoast_head":"\n
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