{"id":302900,"date":"2024-01-16T15:59:40","date_gmt":"2024-01-16T08:59:40","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=302900"},"modified":"2024-01-16T15:59:40","modified_gmt":"2024-01-16T08:59:40","slug":"the-tich-khoi-tru","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-tru\/","title":{"rendered":"H\u01b0\u1edbng d\u1eabn c\u00e1ch t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 v\u00e0 b\u00e0i t\u1eadp minh ho\u1ea1"},"content":{"rendered":"<p><b>Th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5<\/b><span style=\"font-weight: 400;\"> l\u00e0 m\u1ed9t trong nh\u1eefng n\u1ed9i dung h\u00ecnh h\u1ecdc kh\u00f4ng gian th\u00fa v\u1ecb, \u1ee9ng d\u1ee5ng \u0111\u01b0\u1ee3c trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y. V\u1eady c\u00f4ng th\u1ee9c t\u00edch th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5 nh\u01b0 th\u1ebf n\u00e0o? M\u1eddi c\u00e1c b\u1ea1n theo d\u00f5i b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y c\u1ee7a Ho\u00e0ng H\u00e0 Mobile \u0111\u1ec3 bi\u1ebft th\u00eam nh\u1eefng th\u00f4ng tin chi ti\u1ebft nh\u00e9!\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Kh\u1ed1i tr\u1ee5 l\u00e0 g\u00ec?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Kh\u1ed1i tr\u1ee5 hay \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00ecnh tr\u1ee5 l\u00e0 m\u1ed9t h\u00ecnh h\u1ecdc kh\u00f4ng gian \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 \u0111\u01b0\u1eddng k\u00ednh b\u1eb1ng nhau v\u00e0 m\u1eb7t tr\u1ee5. Theo \u0111\u1ecbnh ngh\u0129a trong s\u00e1ch To\u00e1n h\u00ecnh h\u1ecdc l\u1edbp 9, h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a nh\u01b0 sau:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cH\u00ecnh tr\u1ee5 l\u00e0 h\u00ecnh gi\u1edbi b\u1ea1n b\u1edfi m\u1eb7t tr\u1ee5 v\u00e0 hai \u0111\u01b0\u1eddng tr\u00f2n b\u1eb1ng nhau, l\u00e0 giao tuy\u1ebfn c\u1ee7a m\u1eb7t tr\u1ee5 v\u00e0 2 m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi tr\u1ee5c.\u201d<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u201cH\u00ecnh tr\u1ee5 l\u00e0 h\u00ecnh tr\u00f2n xoay khi sinh b\u1edfi b\u1ed1n c\u1ea1nh c\u1ee7a h\u00ecnh m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt khi quay xung quanh m\u1ed9t \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt \u0111\u00f3.\u201d<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-303469 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-2.jpg\" alt=\"the-tich-khoi-tru-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">D\u1ef1a v\u00e0o \u0111\u1ecbnh ngh\u0129a tr\u00ean, \u0111\u1ec3 nh\u1eadn bi\u1ebft h\u00ecnh tr\u1ee5 v\u00e0 t\u00ednh <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5<\/b><span style=\"font-weight: 400;\"> r\u1ea5t \u0111\u01a1n gi\u1ea3n d\u1ef1a v\u00e0o nh\u1eefng t\u00edch ch\u1ea5t sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00ecnh c\u00f3 hai c\u1ea1nh \u0111\u00e1y l\u00e0 h\u00ecnh tr\u00f2n v\u1edbi \u0111\u01b0\u1eddng k\u00ednh b\u1eb1ng nhau l\u00e0 h\u00ecnh tr\u1ee5.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00ecnh tr\u1ee5 c\u00f3 \u0111\u1ed9 d\u00e0i hai song song v\u00e0 b\u1eb1ng nhau.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tr\u1ee5c to\u1ea1 \u0111\u1ed9 c\u1ee7a h\u00ecnh tr\u1ee5 ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng n\u1ed1i t\u1eeb hai t\u00e2m c\u1ee7a m\u1eb7t \u0111\u00e1y ch\u00ednh.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng sinh c\u1ee7a h\u00ecnh tr\u1ee5 ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 c\u00f9ng \u0111\u1ed9 d\u00e0i v\u00e0 song song v\u1edbi tr\u1ee5c to\u1ea1 \u0111\u1ed9.\u00a0<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 c\u00f4ng th\u1ee9c t\u00ednh h\u00ecnh tr\u1ee5 c\u01a1 b\u1ea3n\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">H\u00ecnh tr\u1ee5 s\u1edf h\u1eefu nhi\u1ec1u t\u00ednh n\u0103ng v\u01b0\u1ee3t tr\u1ed9i nh\u01b0 kh\u1ea3 n\u0103ng ch\u1ecbu l\u1ef1c, l\u01b0u tr\u1eef kh\u00f4ng gian t\u1ed1t h\u01a1n so v\u1edbi nh\u1eefng h\u00ecnh kh\u00e1c. V\u00ec v\u1eady, trong cu\u1ed9c s\u1ed1ng ch\u00fang ta b\u1eaft g\u1eb7p r\u1ea5t nhi\u1ec1u v\u1eadt d\u1ee5ng c\u00f3 h\u00ecnh tr\u1ee5 nh\u01b0 lon n\u01b0\u1edbc, c\u1ed9t tr\u1ee5, \u1ed1ng kh\u00f3i, \u0111\u01b0\u1eddng \u1ed1ng,&#8230; V\u1edbi h\u00ecnh h\u1ecdc kh\u00f4ng gian n\u00e0y, m\u1ecdi ng\u01b0\u1eddi c\u00f3 th\u1ec3 t\u00ednh di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n v\u00e0 <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i l\u0103ng tr\u1ee5, th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5<\/b><span style=\"font-weight: 400;\">. Sau \u0111\u00e2y ch\u00fang t\u00f4i s\u1ebd t\u1ed5ng h\u1ee3p nh\u1eefng c\u00f4ng th\u1ee9c v\u1ec1 h\u00ecnh tr\u1ee5 cho c\u00e1c b\u1ea1n n\u1eafm \u0111\u01b0\u1ee3c:\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">T\u00ednh di\u1ec7n t\u00edch xung quanh\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c \u0111\u1ea7u ti\u00ean li\u00ean quan \u0111\u1ebfn h\u00ecnh tr\u1ee5 l\u00e0 c\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh t\u1ee9c l\u00e0 ph\u1ea7n di\u1ec7n t\u00edch m\u1eb7t bao quanh, kh\u00f4ng bao g\u1ed3m m\u1eb7t \u0111\u00e1y. C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh tr\u1ee5 l\u00e0 l\u1ea5y chu vi m\u1eb7t \u0111\u00e1y nh\u00e2n v\u1edbi chi\u1ec1u cao:\u00a0<\/span><\/p>\n<p><strong>Sxq = 2.\u03a0.R.H<\/strong><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"size-full wp-image-303470 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-3.jpg\" alt=\"the-tich-khoi-tru-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">Sxq: Vi\u1ebft t\u1eaft c\u1ee7a c\u1ee5m t\u1eeb di\u1ec7n t\u00edch xung quanh h\u00ecnh tr\u1ee5.\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">2\u03c0r: Chu vi \u0111\u01b0\u1eddng tr\u00f2n m\u1eb7t \u0111\u00e1y h\u00ecnh tr\u1ee5 (\u03c0 = 3,14).\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">h: Chi\u1ec1u cao c\u1ee7a h\u00ecnh tr\u1ee5 c\u1ea7n t\u00ednh.\u00a0<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">T\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u c\u00e1ch t\u00ednh <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5<\/b><span style=\"font-weight: 400;\">, ch\u00fang ta t\u00ecm hi\u1ec3u c\u00e1ch t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n. Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n ch\u00ednh l\u00e0 di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch m\u1eb7t \u0111\u00e1y. C\u00e1ch t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh tr\u1ee5 s\u1ebd l\u1ea5y di\u1ec7n t\u00edch xung quanh c\u1ed9ng v\u1edbi di\u1ec7n t\u00edch hai \u0111\u00e1y.\u00a0<\/span><\/p>\n<p><strong>STP = 2.\u03a0.R\u00b2 + 2\u03c0rh<\/strong><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"size-full wp-image-303471 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-4.jpg\" alt=\"the-tich-khoi-tru-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">STP: Vi\u1ebft t\u1eaft c\u1ee7a c\u1ee5m t\u1eeb di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh tr\u1ee5.\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">2.\u03a0.R\u00b2: Di\u1ec7n t\u00edch c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y (\u03c0 = 3,14).\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">2\u03c0rh: Di\u1ec7n t\u00edch xung quanh h\u00ecnh \u0111\u00e1y c\u1ee7a h\u00ecnh tr\u1ee5.\u00a0<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">T\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh tr\u1ee5 \u0111\u1ec3 bi\u1ebft l\u01b0\u1ee3ng kh\u00f4ng gian l\u01b0u tr\u1eef \u0111\u01b0\u1ee3c bao nhi\u00eau. C\u00e1ch t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 r\u1ea5t \u0111\u01a1n gi\u1ea3n, c\u00e1c b\u1ea1n ch\u1ec9 c\u1ea7n l\u1ea5y di\u1ec7n t\u00edch \u0111\u00e1y nh\u00e2n v\u1edbi chi\u1ec1u cao.\u00a0<\/span><\/p>\n<p><strong>V = \u03a0.R\u00b2.H\u00a0<\/strong><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-303473 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-5.jpg\" alt=\"the-tich-khoi-tru-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">V: Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh tr\u1ee5 c\u1ea7n t\u00ednh.\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">\u03c0r\u00b2: Di\u1ec7n t\u00edch \u0111\u00e1y h\u00ecnh tr\u1ee5.\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">h: Chi\u1ec1u cao c\u1ee7a h\u00ecnh tr\u1ee5.\u00a0<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">D\u1ef1a v\u00e0o c\u00f4ng th\u1ee9c tr\u00ean, c\u00f3 th\u1ec3 th\u1ea5y th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5 ph\u1ee5 thu\u1ed9c v\u00e0o chi\u1ec1u cao, b\u00e1n h\u00ecnh \u0111\u00e1y, s\u1ed1 pi. C\u00e1c b\u1ea1n c\u1ea7n \u00e1p d\u1ee5ng \u0111\u00fang c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00ednh ch\u00ednh x\u00e1c nh\u1ea5t.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Theo c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5 c\u00f3 ba \u0111\u1ea1i l\u01b0\u1ee3ng g\u1ed3m chi\u1ec1u cao, b\u00e1n k\u00ednh \u0111\u00e1y v\u00e0 th\u1ec3 t\u00edch. V\u1edbi ph\u1ea7n th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5 c\u00f3 ph\u1ea7n kh\u00f3 hi\u1ec3u h\u01a1n, do \u0111\u00f3 ch\u00fang t\u00f4i s\u1ebd l\u1ea5y b\u00e0i t\u1eadp minh ho\u1ea1 c\u1ee5 th\u1ec3 cho c\u00e1c b\u1ea1n tham kh\u1ea3o:\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i 1<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Cho h\u00ecnh ch\u1eef nh\u1eadt ABCD trong \u0111\u00f3 c\u00f3 c\u1ea1nh AB = a, g\u00f3c BDC = 30 \u0111\u1ed9. H\u00e3y quay h\u00ecnh ch\u1eef nh\u1eadt n\u00e0y xung quanh c\u1ea1nh AD \u0111\u1ec3 t\u1ea1o th\u00e0nh h\u00ecnh tr\u1ee5. Y\u00eau c\u1ea7u t\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh tr\u1ee5 \u0111\u00f3?\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-303475 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-6.jpg\" alt=\"the-tich-khoi-tru-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed1i v\u1edbi c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp h\u00ecnh h\u1ecdc kh\u00f4ng gian, c\u00e1c b\u1ea1n c\u1ea7n v\u1ebd h\u00ecnh d\u1ef1a tr\u00ean d\u1eef li\u1ec7u c\u1ee7a \u0111\u1ec1 b\u00e0i. \u0110\u1ea7u ti\u00ean, c\u00e1c b\u1ea1n h\u00e3y v\u1ebd h\u00ecnh ch\u1eef nh\u1eadt sau \u0111\u00f3 quay h\u00ecnh ch\u1eef nh\u1eadt xung quanh c\u1ea1nh AD \u0111\u1ec3 t\u1ea1o \u0111\u01b0\u1ee3c h\u00ecnh tr\u1ee5 nh\u01b0 tr\u00ean.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Theo \u0111\u00f3 ta c\u00f3 b\u00e1n h\u00ecnh \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng AB = a<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng cao c\u1ee7a h\u00ecnh tr\u1ee5 b\u1eb1ng BC =\u00a0 CD.tan30 \u0111\u1ed9 = <\/span><span style=\"font-weight: 400;\"> \u00a0a.1\/\u221a3 = a\/\u221a3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00e2y, ch\u00fang ta s\u1ebd suy ra di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh tr\u1ee5 s\u1ebd b\u1eb1ng Sxq = 2rh = 2.3,14.a = a\/\u221a3= (2.3,14.a.2)\/\u221a3<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i 2\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Cho h\u00ecnh t\u1ee9 di\u1ec7n \u0111\u1ec1u ABCD c\u00f3 c\u1ea1nh a, x\u00e9t h\u00ecnh tr\u1ee5 c\u00f3 m\u1ed9t \u0111\u00e1y v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC, chi\u1ec1u cao b\u1eb1ng chi\u1ec1u cao h\u00ecnh t\u1ee9 di\u1ec7n. H\u00e3y t\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a kh\u1ed1i tr\u1ee5 \u0111\u00f3?\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-303476 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-7.jpg\" alt=\"the-tich-khoi-tru-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady, b\u00e0i n\u00e0y y\u00eau c\u1ea7u t\u00ednh di\u1ec7n t\u00edch xung quanh thay v\u00ec <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i l\u0103ng tr\u1ee5, th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5<\/b><span style=\"font-weight: 400;\">. Tr\u01b0\u1edbc ti\u00ean c\u1ea7n g\u1ecdi O l\u00e0 t\u00e2m c\u1ee7a tam gi\u00e1c ABC v\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC l\u00e0 M. The \u0111\u00f3, O s\u1ebd l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp ho\u1eb7c ngo\u1ea1i ti\u1ebfp c\u1ee7a tam gi\u00e1c ABC b\u1edfi \u0111\u00e2y l\u00e0 tam gi\u00e1c \u0111\u1ec1u.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3 c\u1ea1nh AM = AM.sinC = a.sin60 \u0111\u1ed9\u00a0 <\/span><span style=\"font-weight: 400;\">= a\u221a3\/2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">AO = <\/span><span style=\"font-weight: 400;\">2\/<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">AM<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">2\/<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> x <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">\u221a3\/2<\/span><span style=\"font-weight: 400;\">\u00a0= <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">\u221a3\/3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ti\u1ebfp theo, ch\u00fang ta s\u1ebd t\u00ednh chi\u1ec1u cao t\u1ee9 di\u1ec7n:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">h = DO = \u221a(DA2 &#8211; OA2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">\u221a(a2 &#8211; (a\u221a3\/3)2 = a\u221a6\/3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 sau:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">r = OM = AM\/3 = a\u221a3\/6<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sau khi t\u00ednh \u0111\u01b0\u1ee3c chi\u1ec1u cao, b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n, ch\u00fang ta s\u1ebd t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh tr\u1ee5:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sxq = 2.3,14<\/span><span style=\"font-weight: 400;\">rh\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 2.3,14.a\u221a3\/6.a\u221a6\/3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 3,14xa2\u221a2\/3<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i 3<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Cho h\u00ecnh tr\u1ee5 c\u00f3 hai \u0111\u00e1y h\u00ecnh tr\u00f2n t\u00e2m (O) v\u00e0 (O\u2019), t\u1ea1i \u0111\u01b0\u1eddng tr\u00f2n l\u1ea5y \u0111i\u1ec3m A, B sao cho g\u00f3c gi\u1eefa AB v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y b\u1eb1ng 45 \u0111\u1ed9 v\u00e0 c\u00e1ch OO\u2019 b\u1eb1ng a\u221a2\/2 <\/span><span style=\"font-weight: 400;\">. H\u00e3y t\u00ednh <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5<\/b><span style=\"font-weight: 400;\"> theo b\u00e1n k\u00ednh \u0111\u00e1y a.\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-303477 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-8.jpg\" alt=\"the-tich-khoi-tru-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ea7u ti\u00ean, ch\u00fang ta \u0111\u1eb7t OO\u2019 = h sau \u0111\u00f3 g\u1ecdi c\u00e1c \u0111i\u1ec3m I, E, D l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC, BA, OO\u2019.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">D\u1ef1a v\u00e0o \u0111\u00e2y, ta c\u00f3 d(AB,OO&#8217;) = ED = IO&#8217; = <\/span><span style=\"font-weight: 400;\">a\u221a2\/2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Do ABC l\u00e0 tam gi\u00e1c vu\u00f4ng t\u1ea1i C n\u00ean c\u00f3 g\u00f3c B b\u1eb1ng 45 \u0111\u1ed9 -&gt; ABC l\u00e0 tam gi\u00e1c vu\u00f4ng c\u00e2n. Theo \u0111\u00f3, c\u1ea1nh BC = AC = h.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta c\u00f3:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">CO<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">CI<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">+<\/span><span style=\"font-weight: 400;\">IO2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">(<\/span><span style=\"font-weight: 400;\">h\/2)2 + (a\u221a2\/2)2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">h=a<\/span><span style=\"font-weight: 400;\">\u221a2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">D\u1ef1a v\u00e0o nh\u1eefng d\u1eef li\u1ec7u tr\u00ean, th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 b\u1eb1ng <\/span><span style=\"font-weight: 400;\">V = \u03c0a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">.a \u221a2 = \u03c0a<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">\u221a2<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Gi\u1ea3i \u0111\u00e1p c\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">T\u1edbi \u0111\u00e2y, ch\u1eafc h\u1eb3n m\u1ecdi ng\u01b0\u1eddi \u0111\u00e3 bi\u1ebft c\u00e1ch t\u00ednh <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5<\/b><span style=\"font-weight: 400;\"> c\u0169ng nh\u01b0 di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh h\u1ecdc n\u00e0y. V\u1ec1 c\u01a1 b\u1ea3n, c\u00e1ch t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 r\u1ea5t \u0111\u01a1n gi\u1ea3n, c\u00e1c b\u1ea1n c\u1ea7n n\u1eafm \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp li\u00ean quan. Sau \u0111\u00e2y, ch\u00fang t\u00f4i s\u1ebd gi\u1ea3i \u0111\u00e1p nh\u1eefng c\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 h\u00ecnh tr\u1ee5 cho c\u00e1c b\u1ea1n tham kh\u1ea3o nh\u00e9!\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">Th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng th\u1ef1c th\u1ebf n\u00e0o?\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Trong th\u1ef1c t\u1ebf, h\u00ecnh tr\u1ee5 \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng \u0111a d\u1ea1ng ch\u1eb3ng h\u1ea1n nh\u01b0 trong x\u00e2y d\u1ef1ng, s\u1ea3n xu\u1ea5t, gi\u00e1o d\u1ee5c,&#8230; Do \u0111\u00f3, vi\u1ec7c n\u1eafm \u0111\u01b0\u1ee3c c\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n, th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 l\u00e0 v\u00f4 c\u00f9ng c\u1ea7n thi\u1ebft. C\u1ee5 th\u1ec3:\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">Trong x\u00e2y d\u1ef1ng c\u1ea7n t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh s\u1ed1 l\u01b0\u1ee3ng v\u1eadt li\u1ec7u b\u00ea t\u00f4ng, xi m\u0103ng, c\u1ed1t th\u00e9p \u0111\u1ec3 l\u1ea5p \u0111\u1ea7y kh\u1ed1i kh\u00f4ng gian b\u00ean trong.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Trong ng\u00e0nh c\u00f4ng nghi\u1ec7p, t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 gi\u00fap b\u1ea1n bi\u1ebft \u0111\u01b0\u1ee3c n\u00f3 ch\u1ee9a \u0111\u01b0\u1ee3c bao nhi\u00eau ch\u1ea5t l\u1ecfng, ch\u1ea5t b\u1ed9, ch\u1ee9a ga.\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Trong s\u1ea3n xu\u1ea5t, khi thi\u1ebft k\u1ebf c\u00e1c chi ti\u1ebft h\u00ecnh tr\u1ee5 c\u1ea7n t\u00ednh th\u1ec3 t\u00edch \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh dung t\u00edch c\u0169ng nh\u01b0 kh\u1ed1i l\u01b0\u1ee3ng c\u1ee7a n\u00f3.\u00a0<\/span><\/li>\n<li><span style=\"font-weight: 400;\">Trong gi\u00e1o d\u1ee5c, h\u00ecnh tr\u1ee5 l\u00e0 m\u1ed9t trong nh\u1eefng n\u1ed9i dung quan tr\u1ecdng c\u1ee7a h\u00ecnh h\u1ecdc kh\u00f4ng gian. C\u00e1c b\u1ea1n h\u1ecdc sinh l\u1edbp 9 s\u1ebd \u0111\u01b0\u1ee3c ti\u1ebfp x\u00fac v\u1edbi d\u1ea1ng b\u00e0i t\u1eadp n\u00e0y r\u1ed3i ph\u00e1t tri\u1ec3n l\u00ean c\u00e1c l\u1edbp ti\u1ebfp theo.\u00a0<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-10-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-10-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-306702 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-10.jpg\" alt=\"the-tich-khoi-tru-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3><span style=\"font-weight: 400;\">H\u00ecnh tr\u1ee5 v\u1edbi \u0111\u00e1y kh\u00f4ng ph\u1ea3i h\u00ecnh tr\u00f2n c\u00f3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch kh\u00f4ng?\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Trong m\u1ed9t s\u1ed1 tr\u01b0\u1eddng h\u1ee3p, h\u00ecnh tr\u1ee5 c\u00f3 \u0111\u00e1y kh\u00f4ng ph\u1ea3i l\u00e0 h\u00ecnh tr\u00f2n, c\u00e1c b\u1ea1n v\u1eabn c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch c\u1ee7a n\u00f3. C\u00e1c b\u1ea1n c\u1ea7n t\u00ecm di\u1ec7n t\u00edch \u0111\u00e1y, chi\u1ec1u cao c\u1ee7a h\u00ecnh tr\u1ee5 \u0111\u00f3 sau \u0111\u00f3 t\u00ednh<\/span><b> th\u1ec3 t\u00edch kh\u1ed1i l\u0103ng tr\u1ee5, th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 <\/b><span style=\"font-weight: 400;\">nh\u01b0 b\u00ecnh th\u01b0\u1eddng.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch \u0111\u00e1y c\u1ee7a h\u00ecnh tr\u1ee5 s\u1ebd t\u01b0\u01a1ng \u1ee9ng v\u1edbi di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh t\u01b0\u01a1ng \u1ee9ng ch\u1eb3ng h\u1ea1n nh\u01b0 \u0111\u00e1y h\u00ecnh tr\u1ee5 l\u00e0 h\u00ecnh vu\u00f4ng th\u00ec ta t\u00ednh di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng c\u1ea1nh \u0111\u00e1y.\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-11.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-11-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-11-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-306703 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-11.jpg\" alt=\"the-tich-khoi-tru-11\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-11.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-11-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-11-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Chi\u1ec1u cao c\u1ee7a kh\u1ed1i tr\u1ee5 b\u1eb1ng kho\u1ea3ng c\u00e1ch t\u1eeb m\u1eb7t \u0111\u00e1y l\u00ean \u0111\u1ec9nh c\u1ee7a kh\u1ed1i tr\u1ee5.\u00a0<\/span><span style=\"font-weight: 400;\">Cu\u1ed1i c\u00f9ng, ta s\u1ebd t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 b\u1eb1ng di\u1ec7n t\u00edch \u0111\u00e1y nh\u00e2n v\u1edbi chi\u1ec1u cao. L\u01b0u \u00fd, n\u1ebfu \u0111\u00e1y c\u1ee7a h\u00ecnh tr\u1ee5 kh\u00f4ng ph\u1ea3i l\u00e0 h\u00ecnh tr\u00f2n s\u1ebd l\u1ea5y di\u1ec7n t\u00edch \u0111\u00e1y t\u01b0\u01a1ng \u1ee9ng.\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c \u0111\u01b0\u1ee3c kh\u00f4ng?\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh tr\u1ee5 ph\u00eda tr\u00ean, c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u00ednh th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u01b0\u1eddng cong, c\u00f4ng th\u1ee9c ti\u1ebfp tuy\u1ebfn, ph\u01b0\u01a1ng ph\u00e1p c\u1eaft gh\u00e9p,&#8230; Tuy nhi\u00ean c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u00ednh h\u00ecnh tr\u1ee5 kh\u00e1c s\u1ebd ph\u1ee9c t\u1ea1p h\u01a1n. M\u1ed9t s\u1ed1 ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00ednh h\u00ecnh tr\u1ee5 nh\u01b0:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">N\u1ebfu h\u00ecnh tr\u1ee5 b\u1ea1n \u0111ang t\u00ecm th\u1ec3 t\u00edch c\u00f3 h\u00ecnh d\u1ea1ng \u0111\u1eb7c bi\u1ec7t nh\u01b0 h\u00ecnh xo\u1eafn \u1ed1c, c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng t\u00edch ph\u00e2n \u0111\u1ec3 t\u00ecm th\u1ec3 t\u00edch. Theo \u0111\u00f3, t\u00edch ph\u00e2n c\u1ee7a \u0111\u01b0\u1eddng xo\u1eafn \u1ed1c ch\u00ednh l\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh tr\u1ee5 c\u1ea7n t\u00ecm.\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/the-tich-khoi-tru-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-303480 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-9.jpg\" alt=\"the-tich-khoi-tru-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/the-tich-khoi-tru-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">N\u1ebfu c\u00e1c b\u1ea1n bi\u1ebft bi\u1ec3u th\u1ee9c \u0111\u01b0\u1eddng cong c\u1ee7a h\u00ecnh tr\u1ee5 th\u00ec c\u00f3 th\u1ec3 l\u1ef1a ch\u1ecdn c\u00f4ng th\u1ee9c ti\u1ebfp tuy\u1ebfn \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed1i v\u1edbi h\u00ecnh tr\u1ee5 c\u00f3 c\u1ea1nh kh\u00f4ng \u0111\u1ec1u th\u00ec b\u1ea1n c\u00f3 th\u1ec3 c\u1eaft, gh\u00e9p chia nh\u1ecf th\u00e0nh c\u00e1c h\u00ecnh d\u1ea1ng \u0111\u01a1n gi\u1ea3n nh\u01b0 h\u00ecnh tr\u00f2n, tam gi\u00e1c, ch\u1eef nh\u1eadt,&#8230; Ti\u1ebfp theo t\u00ednh th\u1ec3 t\u00edch c\u1ee7a t\u1eebng h\u00ecnh r\u1ed3i c\u1ed9ng l\u1ea1i \u0111\u1ec3 t\u00ecm \u0111\u01b0\u1ee3c <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 <\/b><span style=\"font-weight: 400;\">ban \u0111\u1ea7u.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">L\u01b0u \u00fd, tu\u1ef3 v\u00e0o \u0111\u1eb7c \u0111i\u1ec3m, h\u00ecnh d\u1ea1ng c\u1ee7a h\u00ecnh tr\u1ee5 \u0111\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p t\u00ednh th\u1ec3 t\u00edch ph\u00f9 h\u1ee3p. Th\u00f4ng th\u01b0\u1eddng, c\u00e1c b\u00e0i t\u1eadp \u1edf tr\u00ean l\u1edbp, th\u1ea7y c\u00f4 s\u1ebd cho h\u00ecnh tr\u1ee5 c\u00f3 c\u00e1ch t\u00ednh th\u1ec3 t\u00edch l\u1ea5y chi\u1ec1u cao nh\u00e2n v\u1edbi b\u00ecnh ph\u01b0\u01a1ng \u0111\u1ed9 d\u00e0i b\u00e1n k\u00ednh m\u1eb7t \u0111\u00e1y v\u00e0 s\u1ed1 pi.\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">\u0110\u1eb7t tr\u1ecdng t\u00e2m \u1edf m\u1ed9t v\u1ecb tr\u00ed kh\u00e1c c\u00f3 thay \u0111\u1ed5i th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 kh\u00f4ng?\u00a0<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Khi \u0111\u1eb7t tr\u1ecdng t\u00e2m c\u1ee7a h\u00ecnh tr\u1ee5 \u1edf m\u1ed9t v\u1ecb tr\u00ed kh\u00e1c th\u00ec th\u1ec3 t\u00edch c\u1ee7a ch\u00fang v\u1eabn kh\u00f4ng thay \u0111\u1ed5i. B\u1edfi <\/span><b>th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 <\/b><span style=\"font-weight: 400;\">ch\u1ec9 ph\u1ee5 thu\u1ed9c v\u00e0o b\u00e1n k\u00ednh m\u1eb7t \u0111\u00e1y, chi\u1ec1u cao n\u00ean thay \u0111\u1ed5i v\u1ecb tr\u00ed tr\u1ecdng t\u00e2m kh\u00f4ng \u1ea3nh h\u01b0\u1edfng. Tuy nhi\u00ean, s\u1ef1 thay \u0111\u1ed5i n\u00e0y s\u1ebd \u1ea3nh h\u01b0\u1edfng t\u1edbi t\u01b0 th\u1ebf v\u00e0 t\u00ednh \u1ed5n \u0111\u1ecbnh c\u1ee7a h\u00ecnh tr\u1ee5. C\u00e1c b\u1ea1n h\u00e3y nh\u1edb \u0111i\u1ec1u n\u00e0y \u0111\u1ec3 kh\u00f4ng l\u00e0m sai b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn t\u00ednh th\u1ec3 t\u00edch nh\u00e9!\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">T\u1ea1m K\u1ebft\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady, ch\u00fang t\u00f4i \u0111\u00e3 h\u01b0\u1edbng d\u1eabn c\u00e1ch t\u00ednh<\/span><b> th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 <\/b><span style=\"font-weight: 400;\">cho c\u00e1c b\u1ea1n tham kh\u1ea3o. \u0110\u00e2y l\u00e0 m\u1ed9t n\u1ed9i dung quan tr\u1ecdng trong ph\u1ea7n h\u00ecnh h\u1ecdc kh\u00f4ng gian m\u00e0 m\u1ecdi ng\u01b0\u1eddi c\u1ea7n n\u1eafm \u0111\u01b0\u1ee3c. Ngo\u00e0i c\u00e1ch t\u00ednh th\u1ec3 t\u00edch, ch\u00fang t\u00f4i c\u00f2n h\u01b0\u1edbng d\u1eabn t\u00ednh di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh tr\u1ee5. Mong r\u1eb1ng nh\u1eefng th\u00f4ng tin tr\u00ean gi\u00fap c\u00e1c b\u1ea1n gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i t\u1eadp h\u00ecnh h\u1ecdc m\u1ed9t c\u00e1ch nhanh ch\u00f3ng. Ch\u00fac c\u00e1c b\u1ea1n h\u1ecdc t\u1eadp t\u1ed1t v\u00e0 \u0111\u1ea1t \u0111i\u1ec3m cao trong h\u1ecdc ph\u1ea7n h\u00ecnh h\u1ecdc kh\u00f4ng gian nh\u00e9!\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">H\u00e3y b\u1ea5m theo d\u00f5i fanpage <\/span><b>Ho\u00e0ng H\u00e0 Mobile<\/b><span style=\"font-weight: 400;\"> v\u00e0 k\u00eanh Youtube <\/span><b>Ho\u00e0ng H\u00e0 Channel<\/b><span style=\"font-weight: 400;\"> \u0111\u1ec3 kh\u00f4ng b\u1ecf l\u1ee1 nh\u1eefng th\u00f4ng tin th\u00fa v\u1ecb t\u1eeb ch\u00fang t\u00f4i nh\u00e9!\u00a0<\/span><\/p>\n<p><strong>XEM TH\u00caM:\u00a0<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cach-tinh-dien-tich-tam-giac-deu\/\">T\u00ecm hi\u1ec3u c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh tam gi\u00e1c \u0111\u1ec1u, \u0111\u01b0\u1eddng cao tam gi\u00e1c \u0111\u1ec1u<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/chu-vi-hinh-tu-giac\/\">C\u00f4ng th\u1ee9c t\u00ednh chu vi h\u00ecnh t\u1ee9 gi\u00e1c: L\u00fd thuy\u1ebft, c\u00e1c d\u1ea1ng to\u00e1n v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 l\u00e0 m\u1ed9t trong nh\u1eefng n\u1ed9i dung h\u00ecnh h\u1ecdc kh\u00f4ng gian th\u00fa v\u1ecb, \u1ee9ng d\u1ee5ng \u0111\u01b0\u1ee3c trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y. V\u1eady c\u00f4ng th\u1ee9c t\u00edch th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u1ee5 nh\u01b0 th\u1ebf n\u00e0o? M\u1eddi c\u00e1c b\u1ea1n theo d\u00f5i b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y c\u1ee7a Ho\u00e0ng H\u00e0 Mobile \u0111\u1ec3 bi\u1ebft th\u00eam nh\u1eefng th\u00f4ng tin [&hellip;]<\/p>\n","protected":false},"author":73,"featured_media":303468,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-302900","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>H\u01b0\u1edbng d\u1eabn c\u00e1ch t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 v\u00e0 b\u00e0i t\u1eadp minh ho\u1ea1<\/title>\n<meta name=\"description\" content=\"Th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 th\u1ebf n\u00e0o? H\u01b0\u1edbng d\u1eabn gi\u1ea3i m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u01a1 b\u1ea3n? C\u00f9ng Ho\u00e0ng H\u00e0 Mobile t\u00ecm hi\u1ec3u trong b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y nh\u00e9!\" \/>\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-tru\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"H\u01b0\u1edbng d\u1eabn c\u00e1ch t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 v\u00e0 b\u00e0i t\u1eadp minh ho\u1ea1\" \/>\n<meta property=\"og:description\" content=\"Th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 th\u1ebf n\u00e0o? H\u01b0\u1edbng d\u1eabn gi\u1ea3i m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u01a1 b\u1ea3n? 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