{"id":299722,"date":"2023-12-27T20:47:40","date_gmt":"2023-12-27T13:47:40","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=299722"},"modified":"2025-12-20T14:58:45","modified_gmt":"2025-12-20T07:58:45","slug":"the-tich-khoi-chop","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-chop\/","title":{"rendered":"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u1edbp 8 chi ti\u1ebft nh\u1ea5t"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m l\u1edbp 8 ch\u01b0\u01a1ng H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng &#8211; H\u00ecnh ch\u00f3p \u0111\u1ec1u. C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V = 1\/3 \u00d7 S \u00d7 h (S: di\u1ec7n t\u00edch \u0111\u00e1y vu\u00f4ng, h: chi\u1ec1u cao) v\u00e0 di\u1ec7n t\u00edch xung quanh Sxq = p \u00d7 d (p: n\u1eeda chu vi \u0111\u00e1y, d: trung \u0111o\u1ea1n). B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn chi ti\u1ebft \u0111\u1ecbnh ngh\u0129a, t\u00ednh ch\u1ea5t, v\u00ed d\u1ee5 minh h\u1ecda v\u00e0 b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n \u0111\u1ec3 b\u1ea1n d\u1ec5 d\u00e0ng \u00e1p d\u1ee5ng trong b\u00e0i thi.<\/span><\/p>\n<h2><b>H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u00e0 g\u00ec? T\u00ednh ch\u1ea5t h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">M\u1eb7t \u0111\u00e1y ABCD l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh a.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4 c\u1ea1nh b\u00ean SA = SB = SC = SD.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">4 m\u1eb7t b\u00ean l\u00e0 tam gi\u00e1c c\u00e2n chung \u0111\u1ec9nh S.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng cao SH vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y t\u1ea1i t\u00e2m O c\u1ee7a h\u00ecnh vu\u00f4ng ABCD (giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o)<\/span><span style=\"font-weight: 400;\">.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-299925 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-2.jpg\" alt=\"the-tich-khoi-chop-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Hi\u1ec7n nay hai d\u1ea1ng h\u00ecnh ch\u00f3p th\u01b0\u1eddng g\u1eb7p v\u00e0 t\u00ean g\u1ecdi ph\u1ee5 thu\u1ed9c v\u00e0o h\u00ecnh d\u1ea1ng c\u1ee7a m\u1eb7t ph\u1eb3ng \u0111\u00e1y. \u0110\u00f3 l\u00e0 h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c v\u00e0 h\u00ecnh ch\u00f3p tam gi\u00e1c. B\u00ean c\u1ea1nh \u0111\u00f3, h\u00ecnh ch\u00f3p c\u00f3 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t m\u00e0 c\u00e1c b\u1ea1n c\u1ea7n n\u1eafm nh\u01b0 sau:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00ecnh ch\u00f3p g\u1ed3m nh\u1eefng c\u1ea1nh b\u00ean c\u00f3 \u0111\u1ed9 d\u00e0i nh\u01b0 nhau th\u00ec ch\u00e2n c\u1ee7a \u0111\u01b0\u1eddng cao trong h\u00ecnh ch\u00f3p ch\u00ednh l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1eb1m ngo\u1ea1i ti\u1ebfp v\u1edbi \u0111a gi\u00e1c \u0111\u00e1y.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00ecnh ch\u00f3p g\u1ed3m nh\u1eefng m\u1eb7t b\u00ean c\u00f9ng thi\u1ebft l\u1eadp v\u1edbi \u0111\u00e1y 1 g\u00f3c gi\u1ed1ng nhau th\u00ec ph\u1ea7n ch\u00e2n c\u1ee7a \u0111\u01b0\u1eddng cao h\u00ecnh ch\u00f3p ch\u00ednh l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1eb1m n\u1ed9i ti\u1ebfp v\u1edbi \u0111a gi\u00e1c \u0111\u00e1y.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00ecnh ch\u00f3p g\u1ed3m 1 m\u1eb7t b\u00ean t\u1ea1o g\u00f3c vu\u00f4ng v\u1edbi m\u1eb7t \u0111\u00e1y th\u00ec ph\u1ea7n ch\u00e2n c\u1ee7a \u0111\u01b0\u1eddng cao h\u00ecnh ch\u00f3p ch\u00ednh l\u00e0 ch\u00e2n c\u1ee7a \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c \u0111\u01b0\u1ee3c v\u1ebd t\u1eeb \u0111\u1ec9nh h\u00ecnh ch\u00f3p xu\u1ed1ng d\u01b0\u1edbi c\u1ea1nh \u0111\u00e1y thu\u1ed9c m\u1eb7t b\u00ean n\u00e0y.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Hai m\u1eb7t b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ed3ng th\u1eddi vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y th\u00ec \u0111\u01b0\u1eddng giao tuy\u1ebfn c\u1ee7a hai m\u1eb7t b\u00ean n\u00e0y c\u0169ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y.<\/span><\/li>\n<\/ul>\n<h2><b>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch v\u00e0 di\u1ec7n t\u00edch xung quanh h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u<\/b><\/h2>\n<p><b>Th\u1ec3 t\u00edch:<\/b><span style=\"font-weight: 400;\"> V = 1\/3 \u00d7 S<\/span><i><span style=\"font-weight: 400;\">\u0111\u00e1y \u00d7 h (S<\/span><\/i><span style=\"font-weight: 400;\">\u0111\u00e1y = a\u00b2, h: chi\u1ec1u cao t\u1eeb S \u0111\u1ebfn O)<\/span><\/p>\n<p><b>Di\u1ec7n t\u00edch xung quanh:<\/b><span style=\"font-weight: 400;\"> Sxq = p \u00d7 d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(p = 2a (n\u1eeda chu vi \u0111\u00e1y), d: trung \u0111o\u1ea1n m\u1eb7t b\u00ean)<\/span><\/p>\n<p><b>Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n:<\/b><span style=\"font-weight: 400;\"> Stp = Sxq + S_\u0111\u00e1y<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5 1: H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u1ea1nh \u0111\u00e1y 6cm, h=4cm.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S_\u0111\u00e1y = 6\u00b2 = 36 cm\u00b2 \u2192 V = 1\/3 \u00d7 36 \u00d7 4 = 48 cm\u00b3<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"size-full wp-image-299924 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-1.jpg\" alt=\"the-tich-khoi-chop-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p th\u01b0\u1eddng g\u1eb7p v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Hi\u1ec7n nay c\u00f3 kh\u00e1 nhi\u1ec1u d\u1ea1ng to\u00e1n li\u00ean quan \u0111\u1ebfn vi\u1ec7c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p v\u00ec \u0111\u00e2y l\u00e0 d\u1ea1ng h\u00ecnh h\u1ecdc \u0111\u1eb7c bi\u1ec7t. Sau \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p th\u01b0\u1eddng g\u1eb7p \u0111i k\u00e8m v\u1edbi c\u00e1c b\u00e0i t\u1eadp li\u00ean quan. C\u00e1c b\u1ea1n h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V kh\u1ed1i ch\u00f3p v\u1edbi m\u1eb7t b\u00ean <\/span><span style=\"font-weight: 400;\">\u22a5 v\u1edbi \u0111\u00e1y<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 nh\u1eadn bi\u1ebft d\u1ea1ng b\u00e0i to\u00e1n t\u00ednh th\u1ec3 t\u00edch n\u00e0y th\u00ec c\u00e1c b\u1ea1n c\u1ea7n xem x\u00e9t k\u1ef9 kh\u1ed1i ch\u00f3p m\u00e0 b\u00e0i to\u00e1n \u0111\u01b0a ra. N\u1ebfu nh\u01b0 kh\u1ed1i ch\u00f3p \u0111\u00f3 c\u00f3 2 m\u1eb7t b\u00ean \u0111\u1ed3ng th\u1eddi <\/span><span style=\"font-weight: 400;\">\u22a5 v\u1edbi m\u1eb7t \u0111\u00e1y v\u00e0 \u0111\u01b0\u1eddng cao h\u00ecnh ch\u00f3p c\u0169ng l\u00e0 giao tuy\u1ebfn thu\u1ed9c 2 m\u1eb7t b\u00ean \u0111\u00f3 th\u00ec ch\u00fang ta s\u1ebd \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c gi\u1ea3i n\u00e0y.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 t\u00ednh \u0111\u01b0\u1eddng cao thu\u1ed9c kh\u1ed1i ch\u00f3p th\u00ec c\u00e1c b\u1ea1n h\u00e3y d\u00f9ng \u0111\u1ecbnh l\u00fd nh\u01b0 sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1ch t\u00ednh V h\u00ecnh ch\u00f3p n\u00e0y th\u00ec c\u00e1c b\u1ea1n h\u00e3y xem qua b\u00e0i t\u1eadp minh h\u1ecda nh\u01b0 sau: Cho kh\u1ed1i ch\u00f3p S.ABCD g\u1ed3m m\u1eb7t \u0111\u00e1y l\u00e0 tam gi\u00e1c ABC vu\u00f4ng \u1edf B, m\u1eb7t ph\u1eb3ng t\u00ean SBC \u22a5 v\u1edbi m\u1eb7t ph\u1eb3ng t\u00ean ABC, BC = 4a, BA = 3a. Cho bi\u1ebft g\u00f3c SBC b\u1eb1ng 30 \u0111\u1ed9 v\u00e0 SB b\u1eb1ng 2a\u221a3. H\u00e3y t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.ABC.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"size-full wp-image-299926 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-3.jpg\" alt=\"the-tich-khoi-chop-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u1ea1n h\u00e3y k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng SH sao cho \u22a5 v\u1edbi BC (H ph\u1ea3i n\u1eb1m tr\u00ean c\u1ea1nh BC). Sau \u0111\u00f3 ta c\u00f3:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u1eb7t ph\u1eb3ng SBC <\/span><span style=\"font-weight: 400;\">\u22a5 v\u1edbi m\u1eb7t ph\u1eb3ng ABC<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">BC l\u00e0 \u0111\u01b0\u1eddng giao tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng SBC v\u1edbi m\u1eb7t ph\u1eb3ng ABC<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">SH vu\u00f4ng g\u00f3c v\u1edbi BC<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">SH n\u1eb1m trong m\u1eb7t ph\u1eb3ng SBC<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u2192 SH vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng ABC<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ti\u1ebfp \u0111\u1ebfn ch\u00fang ta x\u00e9t \u0111\u1ebfn tam gi\u00e1c t\u00ean SHB vu\u00f4ng \u1edf H, ta \u0111\u01b0\u1ee3c:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">SH = SB x sin c\u1ee7a g\u00f3c SBC = 2a\u221a3 x sin30 = a\u221a3<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c ABC = 1\/2 x BA x BC = 1\/2 x 3a x 4a = 6a^2<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p S.ABC = 1\/3 x SH x Di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c ABC = 1\/3 x a\u221a3 x 6a^2 = 2a^3\u221a3<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V kh\u1ed1i ch\u00f3p g\u1ed3m c\u1ea1nh b\u00ean \u22a5 v\u1edbi \u0111\u00e1y<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 \u0111\u00e3 \u0111\u1ec1 c\u1eadp \u1edf tr\u00ean th\u00ec c\u00f4ng th\u1ee9c t\u00ednh V h\u00ecnh ch\u00f3p b\u1eb1ng \u2153 S x h. M\u00e0 h\u00ecnh ch\u00f3p c\u00f2n c\u00f3 c\u1ea1nh b\u00ean <\/span><span style=\"font-weight: 400;\">\u22a5 v\u1edbi m\u1eb7t ph\u1eb3ng \u0111\u00e1y th\u00ec c\u00f3 th\u1ec3 suy ra l\u00e0 c\u1ea1nh b\u00ean n\u00e0y ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng cao thu\u1ed9c h\u00ecnh ch\u00f3p v\u1edbi h b\u1eb1ng \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh b\u00ean \u22a5<\/span><span style=\"font-weight: 400;\"> v\u1edbi \u0111\u00e1y. C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 hi\u1ec3u h\u01a1n v\u1ec1 d\u1ea1ng to\u00e1n t\u00ednh V h\u00ecnh ch\u00f3p n\u00e0y qua b\u00e0i t\u1eadp sau:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp: Cho h\u00ecnh ch\u00f3p t\u00ean S.ABC v\u1edbi c\u1ea1nh SA <\/span><span style=\"font-weight: 400;\">\u22a5 v\u1edbi \u0111\u00e1y, \u0111\u1ed9 d\u00e0i SA l\u00e0 4, \u0111\u1ed9 d\u00e0i AB l\u00e0 6, \u0111\u1ed9 d\u00e0i BC l\u00e0 10 v\u00e0 \u0111\u1ed9 d\u00e0i CA l\u00e0 8. V\u1eady t\u00ednh V h\u00ecnh ch\u00f3p S.ABC?<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299927 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-4.jpg\" alt=\"the-tich-khoi-chop-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 AB^2 + AC^2 = 6^2 + 8^2 = BC^2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 Tam gi\u00e1c ABC c\u00f3 g\u00f3c vu\u00f4ng \u1edf A.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ec v\u1eady m\u00e0 di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c n\u00e0y l\u00e0: S = 1\/2 AB x AC = 1\/2 x 6 x 8 = 24<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.ABC = 1\/3 x SA x S c\u1ee7a tam gi\u00e1c ABC = 1\/3 x 4 x 24 = 32<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD v\u1edbi \u0111\u00e1y l\u00e0 1 h\u00ecnh vu\u00f4ng<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">V\u1edbi d\u1ea1ng to\u00e1n h\u00ecnh ch\u00f3p c\u00f3 m\u1eb7t ph\u1eb3ng \u0111\u00e1y l\u00e0 1 h\u00ecnh vu\u00f4ng th\u00ec c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 theo d\u00f5i b\u00e0i t\u1eadp sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp: Cho h\u00ecnh ch\u00f3p S.ABCD g\u1ed3m m\u1eb7t ph\u1eb3ng \u0111\u00e1y l\u00e0 1 h\u00ecnh vu\u00f4ng v\u1edbi \u0111\u1ed9 d\u00e0i c\u1ea1nh l\u00e0 a, c\u1ea1nh SC thi\u1ebft l\u1eadp v\u1edbi m\u1eb7t ph\u1eb3ng SAB 1 g\u00f3c b\u1eb1ng 30 \u0111\u1ed9, c\u1ea1nh SA <\/span><span style=\"font-weight: 400;\">\u22a5 v\u1edbi \u0111\u00e1y. H\u00e3y t\u00ednh V c\u1ee7a kh\u1ed1i ch\u00f3p n\u00e0y?<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299928 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-5.jpg\" alt=\"the-tich-khoi-chop-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">V\u00ec m\u1eb7t ph\u1eb3ng ABCD l\u00e0 1 h\u00ecnh vu\u00f4ng n\u00ean ta c\u00f3 c\u1ea1nh BC vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh AB (1).<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u00e0 c\u1ea1nh SA l\u1ea1i vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng ABCD n\u00ean suy ra c\u1ea1nh SA vu\u00f4ng g\u00f3c v\u1edbi BC (2).<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">T\u1eeb (1) v\u00e0 (2), ch\u00fang ta suy ra c\u1ea1nh BC c\u0169ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng SAB.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">V\u00ec v\u1eady m\u00e0 g\u00f3c t\u1ea1o b\u1edfi c\u1ea1nh SA v\u00e0 m\u1eb7t ph\u1eb3ng SAB = G\u00f3c t\u1ea1o b\u1edfi c\u1ea1nh SC v\u00e0 SB = G\u00f3c CSB = 30 \u0111\u1ed9.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3 suy ra BC\/SB = tan30 = \u221a3\/3\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u2192 SB = \u221a3BC = \u221a3a<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">D\u1ef1a tr\u00ean \u0111\u1ecbnh l\u00fd c\u1ee7a Pitago th\u00ec c\u1ea1nh SA = \u221aSB^2 &#8211; AB^2 = \u221a3a^2 &#8211; a^2 = \u221a2a<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">V\u00ec v\u1eady m\u00e0 th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.ABCD l\u00e0: 1\/3 x SA x S c\u1ee7a h\u00ecnh vu\u00f4ng ABCD = 1\/3 \u221aa x a^2 = (\u221a2\/3) x a^3<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V h\u00ecnh ch\u00f3p d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u00e2y l\u00e0 h\u00ecnh ch\u00f3p kh\u00e1 \u0111\u1eb7c bi\u1ec7t v\u00ec t\u1ea5t c\u1ea3 c\u00e1c m\u1eb7t b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u1ec1u c\u00f3 d\u1ea1ng h\u00ecnh l\u1eadp ph\u01b0\u01a1ng. Do \u0111\u00f3 n\u00ean c\u00e1ch t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng n\u00e0y r\u1ea5t d\u1ec5 d\u00e0ng: V = a x a x a = a^3. Ti\u1ebfp theo l\u00e0 m\u1ed9t b\u00e0i t\u1eadp minh h\u1ecda:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Cho m\u1ed9t h\u00ecnh ch\u00f3p l\u1eadp ph\u01b0\u01a1ng c\u00f3 \u0111\u01b0\u1eddng ch\u00e9o v\u1edbi \u0111\u1ed9 d\u00e0i l\u00e0 27cm. H\u00e3y t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p n\u00e0y?<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299929 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-6.jpg\" alt=\"the-tich-khoi-chop-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a h\u00ecnh ch\u00f3p tr\u00ean l\u00e0 27\/<\/span><span style=\"font-weight: 400;\">\u221a3 (cm).<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u1eady th\u00ec V c\u1ee7a h\u00ecnh ch\u00f3p l\u1eadp ph\u01b0\u01a1ng n\u00e0y b\u1eb1ng V = (27\/\u221a3)^3 = 6561\/\u221a3 (cm^3).<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p l\u0103ng tr\u1ee5 c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c c\u00e2n \u0111\u1ec1u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">N\u1ebfu m\u1ed9t h\u00ecnh ch\u00f3p bao g\u1ed3m m\u1eb7t b\u00ean thu\u1ed9c d\u1ea1ng h\u00ecnh b\u00ecnh h\u00e0nh, 2 m\u1eb7t ph\u1eb3ng \u0111\u00e1y n\u1eb1m song song v\u00e0 c\u00f3 k\u00edch th\u01b0\u1edbc nh\u01b0 nhau th\u00ec n\u00f3 \u0111\u01b0\u1ee3c coi nh\u01b0 h\u00ecnh ch\u00f3p l\u0103ng tr\u1ee5. N\u1ebfu h\u00ecnh ch\u00f3p l\u0103ng tr\u1ee5 n\u00e0y g\u1ed3m m\u1eb7t ph\u1eb3ng \u0111\u00e1y \u0111\u01b0\u1ee3c coi nh\u01b0 tam gi\u00e1c c\u00e2n \u0111\u1ec1u th\u00ec n\u00f3 l\u00e0 h\u00ecnh ch\u00f3p l\u0103ng tr\u1ee5 tam gi\u00e1c c\u00e2n \u0111\u1ec1u. Sau \u0111\u00e2y l\u00e0 b\u00e0i t\u1eadp \u0111\u1ec3 c\u00e1c b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp: Cho 1 h\u00ecnh l\u0103ng tr\u1ee5 l\u00e0 ABC.A\u2019B\u2019C\u2019 c\u00f3 m\u1eb7t ph\u1eb3ng \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u ABC v\u1edbi c\u1ea1nh a b\u1eb1ng 2cm c\u00f9ng chi\u1ec1u cao h b\u1eb1ng 3cm. B\u1ea1n h\u00e3y t\u00ednh to\u00e1n th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p l\u0103ng tr\u1ee5 n\u00e0y?<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299930 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-7.jpg\" alt=\"the-tich-khoi-chop-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u1edfi \u0111\u00e1y c\u1ee7a h\u00ecnh ch\u00f3p tr\u00ean l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u00f3 c\u1ea1nh b\u1eb1ng a n\u00ean S c\u1ee7a tam gi\u00e1c n\u00e0y b\u1eb1ng a^2 x <\/span><span style=\"font-weight: 400;\">\u221a3\/4 = 2^2 x (\u221a3\/4) = \u221a3 (m2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3 suy ra th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p l\u0103ng tr\u1ee5 n\u00e0y b\u1eb1ng S c\u1ee7a tam gi\u00e1c ABC x h\u00a0 = \u221a3 x 3= 3\u221a3 (m3)<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p c\u00f3 \u0111\u00e1y l\u1ee5c gi\u00e1c \u0111\u1ec1u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 hi\u1ec3u h\u01a1n v\u1ec1 c\u00e1ch t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p n\u00e0y th\u00ec m\u1ecdi ng\u01b0\u1eddi xem b\u00e0i t\u1eadp sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp: Cho 1 h\u00ecnh ch\u00f3p c\u00f3 \u0111\u00e1y l\u00e0 l\u1ee5c gi\u00e1c \u0111\u1ec1u v\u1edbi g\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi c\u1ea1nh b\u00ean c\u00f9ng m\u1eb7t ph\u1eb3ng \u0111\u00e1y b\u1eb1ng 30 \u0111\u1ed9, \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y l\u00e0 a. H\u00e3y t\u00ednh V h\u00ecnh ch\u00f3p n\u00e0y?<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299931 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-8.jpg\" alt=\"the-tich-khoi-chop-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta g\u1ecdi t\u00ean c\u1ee7a h\u00ecnh ch\u00f3p \u1edf tr\u00ean l\u00e0 S.ABCDEF, g\u1ecdi O l\u00e0 t\u00e2m thu\u1ed9c m\u1eb7t \u0111\u00e1y ABCDEF.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3 suy ra OA = OC = OB = OD = OF = OE = AB = CD = BC = DE = FA = EF = a<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 Tam gi\u00e1c OAB l\u00e0 1 tam gi\u00e1c c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ec1u l\u00e0 a.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 Di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t \u0111\u00e1y ABCDEF g\u1ea5p 6 l\u1ea7n di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c OAB.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 Di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t \u0111\u00e1y ABCDEF b\u1eb1ng (3.a^2.<\/span><span style=\"font-weight: 400;\">\u221a3)\/2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 c\u1ea1nh SO vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y ABCDEF\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 G\u00f3c \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi c\u1ea1nh SA v\u00e0 m\u1eb7t \u0111\u00e1y = G\u00f3c SAO = 30 \u0111\u1ed9<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 C\u1ea1nh SO = OA x tan30 = (a\u221a3)\/3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.ABCDEF = 1\/3 x Di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t \u0111\u00e1y ABCDEF x SO = 1\/3 x (3.a^2\u221a3)\/2 x (a\u221a3)\/3 = (a^3)\/2<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V h\u00ecnh ch\u00f3p g\u1ed3m c\u1ea1nh b\u00ean \u0111\u00f4i m\u1ed9t \u22a5<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o b\u00e0i t\u1eadp sau \u0111\u1ec3 t\u00ecm hi\u1ec3u v\u1ec1 c\u00e1ch t\u00ednh V h\u00ecnh ch\u00f3p g\u1ed3m c\u1ea1nh b\u00ean \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c v\u1edbi nhau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Cho 1 t\u1ee9 di\u1ec7n S.ABC g\u1ed3m c\u1ea1nh SA, SC, SB v\u00e0 \u0111\u00f4i m\u1ed9t c\u1ea1nh b\u00ean vu\u00f4ng g\u00f3c v\u1edbi nhau. Cho bi\u1ebft SB = 4a, SA = 3a, SC = 5a. H\u00e3y t\u00ednh V h\u00ecnh ch\u00f3p n\u00e0y?<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299932 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-9.jpg\" alt=\"the-tich-khoi-chop-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 c\u1ea1nh SA vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh SC, c\u1ea1nh SA vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh SB \u2192 C\u1ea1nh SA vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng SBC.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3 suy ra di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n S.ABC = 1\/3 x SA x di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t ph\u1eb3ng SBC = 1\/6 x SA x SB x SC = 1\/6 x 3a x 4a x 5a = 10a^3<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">D\u1ea1ng to\u00e1n t\u00ednh V h\u00ecnh ch\u00f3p tr\u00f2n xoay<\/span><\/h3>\n<h4>C\u00f4ng th\u1ee9c t\u00ednh V h\u00ecnh ch\u00f3p tr\u00f2n xoay<\/h4>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p tr\u00f2n xoay g\u1ea7n gi\u1ed1ng v\u1edbi c\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh V h\u00ecnh ch\u00f3p c\u01a1 b\u1ea3n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V = 1\/3 B x h\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 1\/3 x \u03c0 x r^2 x h x 1\/3 x B x h\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 1\/3 x \u03c0 x r^2 x h<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B: Di\u1ec7n t\u00edch c\u1ee7a \u0111\u00e1y c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">r: B\u00e1n k\u00ednh c\u1ee7a m\u1eb7t ph\u1eb3ng \u0111\u00e1y c\u00f3 h\u00ecnh n\u00f3n<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">h: Chi\u1ec1u cao h\u00ecnh n\u00f3n<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-10-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-chop-10-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299933 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-10.jpg\" alt=\"the-tich-khoi-chop-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-chop-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h4>B\u00e0i t\u1eadp t\u00ednh V h\u00ecnh ch\u00f3p tr\u00f2n xoay<\/h4>\n<p><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp sau \u0111\u00e2y s\u1ebd gi\u00fap b\u1ea1n hi\u1ec3u h\u01a1n v\u1ec1 c\u00e1ch t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p tr\u00f2n xoay \u1edf tr\u00ean:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Cho 1 h\u00ecnh n\u00f3n cao 2<\/span><span style=\"font-weight: 400;\">\u221a5 v\u1edbi 1 m\u1eb7t ph\u1eb3ng \u0111i qua ph\u1ea7n \u0111\u1ec9nh c\u1ee7a h\u00ecnh n\u00f3n r\u1ed3i c\u1eaft h\u00ecnh n\u00f3n n\u00e0y th\u00e0nh 1 thi\u1ebft di\u1ec7n c\u00f3 h\u00ecnh tam gi\u00e1c c\u1ea1nh \u0111\u1ec1u v\u1edbi S c\u1ee7a tam gi\u00e1c = 9\u221a3. H\u00e3y t\u00ednh V c\u1ee7a h\u00ecnh ch\u00f3p \u0111\u00e3 \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n theo h\u00ecnh n\u00f3n c\u1ee7a \u0111\u1ec1 b\u00e0i.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 tam gi\u00e1c \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh t\u1eeb thi\u1ebft di\u1ec7n l\u00e0 tam gi\u00e1c ABC gi\u1ed1ng h\u00ecnh sau, \u0111i\u1ec3m I \u0111\u01b0\u1ee3c coi l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC, coi a nh\u01b0 \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh tam gi\u00e1c ABC. Nh\u01b0 v\u1eady, ta c\u00f3:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(a^2\u221a3)\/4 = 9\u221a3 \u2192 (3a^2)\/4 = 27 \u2192 AI = a\u221a3 = 3\u221a3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2192 OI = \u221aAI^2 &#8211; AO^2 = \u221a27 &#8211;\u00a0 20 = \u221a7<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e1n k\u00ednh c\u1ee7a \u0111\u00e1y d\u1ea1ng h\u00ecnh n\u00f3n l\u00e0 R = OC = \u221aOI^2 + IC^2 = \u221a7 + 9 = 4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u1eady th\u00ec V c\u1ee7a h\u00ecnh ch\u00f3p tr\u00ean l\u00e0 V = 1\/3 x <\/span><span style=\"font-weight: 400;\">\u03c0 x 4^2 x 2<\/span><span style=\"font-weight: 400;\">\u221a5 = (32\u221a5<\/span><span style=\"font-weight: 400;\">\u03c0)\/3\u00a0<\/span><\/p>\n<h2 data-start=\"201\" data-end=\"257\">B\u00c0I T\u1eacP T\u1ef0 LUY\u1ec6N: T\u00cdNH TH\u1ec2 T\u00cdCH H\u00ccNH CH\u00d3P T\u1ee8 GI\u00c1C \u0110\u1ec0U<\/h2>\n<h3 data-start=\"259\" data-end=\"268\">B\u00e0i 1<\/h3>\n<p data-start=\"270\" data-end=\"382\"><strong data-start=\"270\" data-end=\"281\">\u0110\u1ec1 b\u00e0i:<\/strong><br data-start=\"281\" data-end=\"284\" \/>Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 c\u1ea1nh \u0111\u00e1y d\u00e0i 6 cm, chi\u1ec1u cao h = 4 cm.<br data-start=\"351\" data-end=\"354\" \/>T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p.<\/p>\n<p data-start=\"384\" data-end=\"488\"><strong data-start=\"384\" data-end=\"397\">L\u1eddi gi\u1ea3i:<\/strong><br data-start=\"397\" data-end=\"400\" \/>H\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng n\u00ean di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0:<br data-start=\"464\" data-end=\"467\" \/>S_\u0111\u00e1y = 6\u00b2 = 36 (cm\u00b2)<\/p>\n<p data-start=\"490\" data-end=\"546\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p:<br data-start=\"524\" data-end=\"527\" \/>V = 1\/3 \u00d7 S_\u0111\u00e1y \u00d7 h<\/p>\n<p data-start=\"548\" data-end=\"600\">Thay s\u1ed1 v\u00e0o c\u00f4ng th\u1ee9c:<br data-start=\"570\" data-end=\"573\" \/>V = 1\/3 \u00d7 36 \u00d7 4 = 48 (cm\u00b3)<\/p>\n<p data-start=\"602\" data-end=\"620\"><strong data-start=\"602\" data-end=\"613\">\u0110\u00e1p s\u1ed1:<\/strong> 48 cm\u00b3<\/p>\n<h3 data-start=\"627\" data-end=\"636\">B\u00e0i 2<\/h3>\n<p data-start=\"638\" data-end=\"761\"><strong data-start=\"638\" data-end=\"649\">\u0110\u1ec1 b\u00e0i:<\/strong><br data-start=\"649\" data-end=\"652\" \/>Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 th\u1ec3 t\u00edch V = 200 cm\u00b3, chi\u1ec1u cao h = 12 cm.<br data-start=\"723\" data-end=\"726\" \/>T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y c\u1ee7a h\u00ecnh ch\u00f3p.<\/p>\n<p data-start=\"763\" data-end=\"901\"><strong data-start=\"763\" data-end=\"776\">L\u1eddi gi\u1ea3i:<\/strong><br data-start=\"776\" data-end=\"779\" \/>G\u1ecdi a l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y c\u1ee7a h\u00ecnh ch\u00f3p.<br data-start=\"818\" data-end=\"821\" \/>V\u00ec h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng n\u00ean di\u1ec7n t\u00edch \u0111\u00e1y l\u00e0:<br data-start=\"888\" data-end=\"891\" \/>S_\u0111\u00e1y = a\u00b2<\/p>\n<p data-start=\"903\" data-end=\"967\">\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p:<br data-start=\"945\" data-end=\"948\" \/>V = 1\/3 \u00d7 S_\u0111\u00e1y \u00d7 h<\/p>\n<p data-start=\"969\" data-end=\"1006\">Thay s\u1ed1 \u0111\u00e3 cho:<br data-start=\"984\" data-end=\"987\" \/>200 = 1\/3 \u00d7 a\u00b2 \u00d7 12<\/p>\n<p data-start=\"1008\" data-end=\"1059\">R\u00fat g\u1ecdn:<br data-start=\"1016\" data-end=\"1019\" \/>200 = 4a\u00b2<br data-start=\"1028\" data-end=\"1031\" \/>a\u00b2 = 50<br data-start=\"1038\" data-end=\"1041\" \/>a = \u221a50 = 5\u221a2 (cm)<\/p>\n<p data-start=\"1061\" data-end=\"1079\"><strong data-start=\"1061\" data-end=\"1072\">\u0110\u00e1p s\u1ed1:<\/strong> 5\u221a2 cm<\/p>\n<p><span style=\"font-weight: 400;\">N\u1ed9i dung tr\u00ean \u0111\u00e3 chia s\u1ebb kh\u00e1 nhi\u1ec1u c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p nhanh ch\u00f3ng cho c\u00e1c b\u1ea1n t\u00ecm hi\u1ec3u. Hy v\u1ecdng c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 gi\u1ea3i to\u00e1n nhanh h\u01a1n v\u1edbi nh\u1eefng c\u00f4ng th\u1ee9c v\u00e0 d\u1ea1ng b\u00e0i t\u1eadp \u1edf tr\u00ean. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng \u0111\u1ec3 c\u00e1c b\u1ea1n h\u1ecdc t\u1ed1t h\u01a1n m\u00f4n h\u00ecnh h\u1ecdc \u1edf b\u1eadc THPT.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Tham kh\u1ea3o b\u00e0i vi\u1ebft li\u00ean quan:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/\">\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec? T\u00ednh ch\u1ea5t, c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i t\u1eadp t\u00ednh \u0111\u01b0\u1eddng trung tuy\u1ebfn<\/a><\/strong><\/li>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-luong-giac\/\">C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c, b\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t<\/a><\/strong><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m l\u1edbp 8 ch\u01b0\u01a1ng H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng &#8211; H\u00ecnh ch\u00f3p \u0111\u1ec1u. C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V = 1\/3 \u00d7 S \u00d7 h (S: di\u1ec7n t\u00edch \u0111\u00e1y vu\u00f4ng, h: chi\u1ec1u cao) v\u00e0 di\u1ec7n t\u00edch xung quanh Sxq = p \u00d7 d (p: n\u1eeda [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":299923,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-299722","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u1edbp 8 (di\u1ec7n t\u00edch xung quanh, v\u00ed d\u1ee5 chi ti\u1ebft)<\/title>\n<meta name=\"description\" content=\"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u1edbp 8: V = 1\/3 S h. H\u01b0\u1edbng d\u1eabn chi ti\u1ebft di\u1ec7n t\u00edch xung quanh Sxq = p.d, v\u00ed d\u1ee5 minh h\u1ecda, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n. H\u1ecdc ngay \u0111\u1ec3 l\u00e0m b\u00e0i h\u00ecnh h\u1ecdc d\u1ec5 d\u00e0ng!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-chop\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u1edbp 8 chi ti\u1ebft nh\u1ea5t\" \/>\n<meta property=\"og:description\" content=\"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u1edbp 8: V = 1\/3 S h. H\u01b0\u1edbng d\u1eabn chi ti\u1ebft di\u1ec7n t\u00edch xung quanh Sxq = p.d, v\u00ed d\u1ee5 minh h\u1ecda, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n. 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