{"id":304886,"date":"2024-01-12T19:56:50","date_gmt":"2024-01-12T12:56:50","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=304886"},"modified":"2026-08-25T15:17:58","modified_gmt":"2026-08-25T08:17:58","slug":"cong-thuc-the-tich-khoi-tron-xoay","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-the-tich-khoi-tron-xoay\/","title":{"rendered":"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay l\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ec1 b\u00e0i to\u00e1n h\u1ecdc c\u1ef1c k\u1ef3 th\u00fa v\u1ecb \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong h\u00ecnh h\u1ecdc kh\u00f4ng gian c\u1ea5p b\u1eadc trung h\u1ecdc. Nh\u1edd v\u00e0o c\u00f4ng th\u1ee9c ch\u00fang ta c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch v\u1eadt th\u1ec3 kh\u1ed1i tr\u00f2n xoay quanh tr\u1ee5c Oy v\u00e0 Ox. Th\u00f4ng qua b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y, h\u00e3y c\u00f9ng Ho\u00e0ng H\u00e0 Mobile t\u00ecm hi\u1ec3u c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay trong h\u00ecnh h\u1ecdc kh\u00f4ng gian v\u00e0 v\u1eadn d\u1ee5ng v\u00e0o th\u1ef1c t\u1ebf nh\u00e9!\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">\u0110\u1ecbnh ngh\u0129a th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u v\u1ec1 c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay th\u00ec b\u1ea1n c\u1ea7n ph\u1ea3i hi\u1ec3u \u0111\u01b0\u1ee3c r\u00f5 r\u00e0ng v\u1ec1 \u0111\u1ecbnh ngh\u0129a kh\u00e1i ni\u1ec7m th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay. Trong h\u00ecnh h\u1ecdc kh\u00f4ng gian, kh\u1ed1i v\u1eadt th\u1ec3 tr\u00f2n xoay \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a \u0111\u00f3 l\u00e0 m\u1ed9t h\u00ecnh kh\u1ed1i \u0111\u01b0\u1ee3c t\u1ea1o ra th\u00f4ng qua vi\u1ec7c xoay xung quanh tr\u1ee5c Ox ho\u1eb7c Oy c\u1ed1 \u0111\u1ecbnh. \u0110\u1ed1i v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh h\u00ecnh h\u1ecdc kh\u00f4ng gian trung h\u1ecdc ph\u1ed5 th\u00f4ng, c\u00e1c b\u1ea1n s\u1ebd \u0111\u01b0\u1ee3c h\u1ecdc v\u1ec1 th\u1ec3 t\u00edch kh\u1ed1i n\u00f3n, kh\u1ed1i tr\u1ee5, kh\u1ed1i c\u1ea7u v\u1eadt th\u1ec3 tr\u00f2n xoay.\u00a0<\/span><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-304895\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1.jpg\" alt=\"\u0110\u1ecbnh ngh\u0129a th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay l\u00e0 g\u00ec?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay d\u00f9ng \u0111\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c to\u00e0n b\u1ed9 th\u1ec3 t\u00edch c\u1ee7a v\u1eadt th\u1ec3 \u0111\u01b0\u1ee3c t\u1ea1o ra th\u00f4ng qua m\u1ed9t \u0111\u01b0\u1eddng cong quay xung quanh m\u1ed9t tr\u1ee5c c\u1ed1 \u0111\u1ecbnh. \u0110\u00e2y l\u00e0 c\u00f4ng th\u1ee9c \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong tr\u01b0\u1eddng h\u1ee3p \u0111\u00f3 l\u00e0 v\u1eadt th\u1ec3 h\u00ecnh d\u1ea1ng tr\u00f2n xoay.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i v\u1eadt th\u1ec3 tr\u00f2n xoay th\u00ec b\u1ea1n c\u1ea7n ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c th\u00f4ng tin v\u1ec1 s\u1ed1 \u0111o \u0111\u01b0\u1eddng cao v\u00e0 tr\u1ee5c quay.\u00a0 Nh\u01b0 v\u1eady, c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u0111\u00f3 l\u00e0: <\/span><b>V = \u03c0 \u222b[a, b] [f(x)]^2 dx. <\/b><span style=\"font-weight: 400;\">Trong \u0111\u00f3 c\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a c\u00f4ng th\u1ee9c \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh nh\u01b0 sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">V \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u00f2n xoay.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u03c0 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 h\u1eb1ng s\u1ed1 pi, c\u00f3 gi\u00e1 tr\u1ecb g\u1ea7n b\u1eb1ng 3.14.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">[a,b] \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 s\u1ed1 \u0111o kho\u1ea3ng c\u00e1ch gi\u1edbi h\u1ea1n \u0111\u01b0\u1eddng cong, ngh\u0129a l\u00e0 s\u1ed1 \u0111o c\u1ee7a ph\u1ea7n [a,b] n\u1eb1m tr\u00ean tr\u1ee5c khi v\u1eadt th\u1ec3 xoay xung quanh.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">f(x) \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 h\u00e0m s\u1ed1 c\u1ea7n \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 \u0111\u01b0\u1eddng cong t\u1ea1o ra kh\u1ed1i tr\u00f2n xoay trong kho\u1ea3ng \u0111\u1ed9 d\u00e0i [a,b].\u00a0<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-304896\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2.jpg\" alt=\"C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay l\u00e0 g\u00ec\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 c\u00f3 th\u1ec3 hi\u1ec3u h\u01a1n, b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o v\u00ed d\u1ee5 d\u01b0\u1edbi \u0111\u00e2y: T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay xung quanh tr\u1ee5c Oy c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh Oy= x^2 n\u1eb1m tr\u00ean kho\u1ea3ng c\u00e1ch t\u1eeb x=0 \u0111\u1ebfn x=4. \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean b\u1ea1n c\u00f3 th\u1ec3 \u0111\u01b0a ra \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 sau:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V = \u03c0 \u222b[0, 4] (x^2)^2 dx = \u03c0 \u222b[0, 4] x^4 dx<\/span><\/p>\n<p><span style=\"font-weight: 400;\">=&gt; V= \u03c0 [x^5\/5] [0, 4] = \u03c0 * (4^5\/5 &#8211; 0^5\/5) = 12\u03c0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3 tr\u00f2n xoay tr\u00ean ta \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 \u0111\u00f3 l\u00e0 12\u03c0.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">\u0110i\u1ec3u ki\u1ec7n c\u1ea7n \u0111\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c n\u00eau tr\u00ean c\u1ea7n ph\u1ea3i \u0111\u00e1p \u1ee9ng \u0111i\u1ec1u ki\u1ec7n c\u1ea7n trong to\u00e1n h\u1ecdc. \u0110i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u00f3 l\u00e0 kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u1ea1o ra th\u00f4ng qua vi\u1ec7c quay xung quanh m\u1ed9t tr\u1ee5c c\u1ed1 \u0111\u1ecbnh. C\u00f3 ngh\u0129a ph\u1ea7n v\u1eadt th\u1ec3 n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t \u0111\u01b0\u1eddng cong c\u1ed1 \u0111\u1ecbnh v\u00e0 xoay xung quanh tr\u1ee5c nh\u1ea5t \u0111\u1ecbnh \u0111\u1ec3 t\u1ea1o ra h\u00ecnh d\u1ea1ng v\u1eadt th\u1ec3 tr\u00f2n xoay. C\u1ee5 th\u1ec3, \u0111\u1ec3 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c kh\u1ed1i tr\u00f2n xoay th\u00ec c\u1ea7n ph\u1ea3i \u0111\u00e1p \u1ee9ng \u0111\u01b0\u1ee3c \u0111\u1ea7y \u0111\u1ee7 c\u00e1c th\u00f4ng tin sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng cong x\u00e1c \u0111\u1ecbnh c\u1ed1 \u0111\u1ecbnh \u0111\u01b0\u1ee3c kh\u1ed1i v\u1eadt th\u1ec3: Ph\u1ea7n \u0111\u01b0\u1eddng cong n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh th\u00f4ng qua m\u1ed9t h\u1ea3m s\u1ed1 bi\u1ec3u di\u1ec5n \u0111\u00f3 l\u00e0 y= f(x) hay x= g(y). Trong \u0111\u00f3 f(x) v\u00e0 g)y) \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh h\u00e0m s\u1ed1 li\u00ean tr\u1ee5c n\u1eb1m trong \u0111o\u1ea1n kho\u1ea3ng c\u00e1ch [a,b] v\u1edbi \u0111i\u1ec1u ki\u1ec7n a &lt; b.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110o\u1ea1n [a,b] l\u00e0 kho\u1ea3ng c\u00e1ch ph\u1ea1m vi c\u1ea7n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh c\u00f3 trong h\u00e0m s\u1ed1 c\u1ee7a c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tr\u1ee5c quanh Ox ho\u1eb7c Oy l\u00e0 k\u00fd hi\u1ec7u \u0111\u1ea1i di\u1ec7n bi\u1ec3u di\u1ec5n cho c\u00e1c tr\u1ee5c c\u1ed1 \u0111\u1ecbnh \u0111\u01b0\u1ee3c kh\u1ed1i tr\u00f2n quay xung quanh.\u00a0<\/span><\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-304897\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3.jpg\" alt=\"\u0110i\u1ec3u ki\u1ec7n c\u1ea7n \u0111\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u00ecn chung, \u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch V c\u1ee7a kh\u1ed1i tr\u00f2n xoay th\u00ec b\u1ea1n c\u1ea7n ph\u1ea3i x\u00e1c \u0111\u1ecbnh ph\u1ea7n \u0111\u01b0\u1eddng cong \u0111\u01b0\u1ee3c \u0111\u1ecbnh h\u00ecnh c\u1ee7a kh\u1ed1i tr\u00f2n. C\u00f9ng v\u1edbi ph\u1ea7n ph\u1ea1m vi x\u00e1c \u0111\u1ecbnh bao g\u1ed3m tr\u1ee5c c\u1ed1 \u0111\u1ecbnh v\u00e0 \u0111\u01b0\u1eddng cong kh\u1ed1i tr\u00f2n quay xung quanh. Cu\u1ed1i c\u00f9ng, \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay d\u1ef1a v\u00e0o h\u00e0m s\u1ed1 \u0111\u01b0\u1eddng xong c\u00f9ng ph\u1ea1m vi \u0111\u00e3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u0111\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch V theo \u0111\u1ec1 b\u00e0i.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c n\u00e0o kh\u00e1c?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c n\u00eau tr\u00ean, v\u1eadt th\u1ec3 tr\u00f2n xoay c\u00f2n \u0111\u01b0\u1ee3c t\u00ednh d\u1ef1a theo c\u00f4ng th\u1ee9c kh\u00e1c. \u0110\u1ea7u ti\u00ean, c\u1ea7n ph\u1ea3i x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c mi\u1ec1n (D) m\u00e0 v\u1eadt th\u1ec3 xoay xung quanh. Khu v\u1ef1c mi\u1ec1n n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi ph\u1ea7n \u0111\u1ed3 th\u00ec bi\u1ec3u di\u1ec5n b\u1edfi ph\u01b0\u01a1ng tr\u00ecnh h\u00e0m s\u1ed1 y= f(x), v\u1edbi \u0111o\u1ea1n th\u1eb3ng h\u00e0m s\u1ed1 x=a, x=b v\u00e0 xoay xung quanh tr\u1ee5c Ox.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ti\u1ebfp theo, ti\u1ebfn h\u00e0nh t\u00ednh di\u1ec7n t\u00edch S \u0111\u01b0\u1ee3c quay xung quanh tr\u1ee5c Ox c\u1ee7a ph\u1ea7n di\u1ec7n t\u00edch gi\u1edbi h\u1ea1n D v\u1edbi c\u00f4ng th\u1ee9c \u0111\u00f3 l\u00e0 <\/span><span style=\"font-weight: 400;\">S = \u222b[a,b] (\u03c0[f(x)]^2)dx. Cu\u1ed1i c\u00f9ng ti\u1ebfn h\u00e0nh t\u00ednh th\u1ec3 t\u00edch V kh\u1ed1i tr\u00f2n xoay b\u1eb1ng c\u00e1ch l\u1ea5y di\u1ec7n t\u00edch \u0111\u00e3 t\u00ednh \u0111\u01b0\u1ee3c nh\u00e2n v\u1edbi chi\u1ec1u d\u00e0i L v\u00f2ng quanh tr\u1ee5c Ox.\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304899\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4.jpg\" alt=\"Th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c n\u00e0o kh\u00e1c\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Do \u0111\u00f3, c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay s\u1ebd \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c kh\u00e1c \u0111\u00f3 l\u00e0: <\/span><b>V= S * L<\/b><span style=\"font-weight: 400;\">. <\/span><span style=\"font-weight: 400;\">Khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c n\u00e0y th\u00ec b\u1ea1n s\u1ebd t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch v\u1edbi v\u1eadt th\u1ec3 kh\u1ed1i tr\u00f2n xoay m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 \u0111\u01a1n gi\u1ea3n h\u01a1n.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">H\u01b0\u1edbng d\u1eabn t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay chi ti\u1ebft\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau khi bi\u1ebft \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay nh\u01b0ng nhi\u1ec1u b\u1ea1n ch\u01b0a n\u1eafm \u0111\u01b0\u1ee3c ngu\u1ed3n g\u1ed1c c\u00e1c b\u01b0\u1edbc chi ti\u1ebft t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 c\u00e1c b\u01b0\u1edbc h\u01b0\u1edbng d\u1eabn chi ti\u1ebft t\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3 tr\u00f2n xoay nh\u01b0 sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 1: \u0110\u1ea7u ti\u00ean, c\u1ea7n x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c khu v\u1ef1c mi\u1ec1n gi\u1edbi h\u1ea1n c\u1ee7a v\u1eadt th\u1ec3 b\u1edfi ph\u01b0\u01a1ng tr\u00ecnh bi\u1ec3u di\u1ec5n h\u00e0m s\u1ed1 ho\u1eb7c \u0111\u01b0\u1eddng cong \u0111\u01b0\u1ee3c v\u1eadt th\u1ec3 quay xung quanh.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 2: Ti\u1ebfp theo, x\u00e1c \u0111\u1ecbnh ph\u1ea7n \u0111o\u1ea1n th\u1eb3ng tr\u1ee5c Ox \u0111\u01b0\u1ee3c kh\u1ed1i tr\u00f2n quay xung quanh. Tr\u1ee5c Ox l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng c\u1ee7a kh\u1ed1i tr\u00f2n.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 3: Sau \u0111\u00f3, ti\u1ebfn h\u00e0nh t\u00ednh di\u1ec7n t\u00edch S ph\u1ea7n mi\u1ec1n gi\u1edbi h\u1ea1n \u0111\u01b0\u1ee3c quay xung quanh tr\u1ee5c Ox, \u0111\u00e2y l\u00e0 ph\u1ea7n di\u1ec7n t\u00edch \u0111\u01b0\u1ee3c t\u1ea1o ra b\u1edfi mi\u1ec1n gi\u1edbi h\u1ea1n khi quay xung quanh tr\u1ee5c Ox.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 4: Ti\u1ebfp theo, \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V kh\u1ed1i tr\u00f2n xoay <\/span><span style=\"font-weight: 400;\">V = \u03c0\u222b(S)dx. Trong \u0111\u00f3, \u03c0 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 s\u1ed1 Pi c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 3.14 v\u00e0 \u222b(S)dx l\u00e0 c\u00f4ng th\u1ee9c t\u00edch ph\u00e2n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh ph\u1ea7n di\u1ec7n t\u00edch S quanh xung quanh tr\u1ee5c X.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u1edbc 5: Cu\u1ed1i c\u00f9ng th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh t\u00ednh ph\u00e2n \u0111\u1ec3 c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh ph\u1ea7n gi\u00e1 tr\u1ecb th\u1ec3 t\u00edch V c\u1ee7a kh\u1ed1i tr\u00f2n xoay.<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304901\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5.jpg\" alt=\"H\u01b0\u1edbng d\u1eabn t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay chi ti\u1ebft\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">Th\u00f4ng qua c\u00e1c b\u01b0\u1edbc tr\u00ean ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c to\u00e0n b\u1ed9 th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i tr\u00f2n xoay c\u1ea7n t\u00ednh.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">V\u00ec sao h\u1ecdc sinh c\u1ea7n ph\u1ea3i n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay l\u00e0 m\u1ed9t trong nh\u1eefng c\u00f4ng th\u1ee9c quan tr\u1ecdng trong to\u00e1n h\u00ecnh h\u1ecdc kh\u00f4ng gian. C\u00f4ng th\u1ee9c n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a c\u00e1c v\u1eadt th\u1ec3 tr\u00f2n xoay, ch\u1eb3ng h\u1ea1n nh\u01b0 h\u00ecnh tr\u1ee5, h\u00ecnh n\u00f3n, h\u00ecnh c\u1ea7u,&#8230; Vi\u1ec7c n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay c\u00f3 nh\u1eefng \u00fd ngh\u0129a quan tr\u1ecdng sau:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Gi\u00fap h\u1ecdc sinh hi\u1ec3u r\u00f5 b\u1ea3n ch\u1ea5t c\u1ee7a kh\u1ed1i tr\u00f2n xoay. C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c suy ra t\u1eeb \u0111\u1ecbnh ngh\u0129a c\u1ee7a th\u1ec3 t\u00edch. Khi h\u1ecdc sinh n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c n\u00e0y, h\u1ecd s\u1ebd hi\u1ec3u \u0111\u01b0\u1ee3c m\u1ed1i quan h\u1ec7 gi\u1eefa th\u1ec3 t\u00edch v\u00e0 c\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a kh\u1ed1i tr\u00f2n xoay, ch\u1eb3ng h\u1ea1n nh\u01b0 b\u00e1n k\u00ednh, chi\u1ec1u cao,&#8230;<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Gi\u00fap h\u1ecdc sinh gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp v\u1ec1 kh\u1ed1i tr\u00f2n xoay m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 nhanh ch\u00f3ng. C\u00e1c b\u00e0i t\u1eadp v\u1ec1 kh\u1ed1i tr\u00f2n xoay th\u01b0\u1eddng c\u00f3 nhi\u1ec1u d\u1ea1ng kh\u00e1c nhau, \u0111\u00f2i h\u1ecfi h\u1ecdc sinh ph\u1ea3i v\u1eadn d\u1ee5ng linh ho\u1ea1t c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 h\u00ecnh h\u1ecdc kh\u00f4ng gian. Khi n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay, h\u1ecdc sinh s\u1ebd d\u1ec5 d\u00e0ng gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp n\u00e0y.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Gi\u00fap h\u1ecdc sinh v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c h\u00ecnh h\u1ecdc kh\u00f4ng gian trong th\u1ef1c t\u1ebf. Kh\u1ed1i tr\u00f2n xoay l\u00e0 m\u1ed9t lo\u1ea1i v\u1eadt th\u1ec3 ph\u1ed5 bi\u1ebfn trong th\u1ef1c t\u1ebf, ch\u1eb3ng h\u1ea1n nh\u01b0 lon n\u01b0\u1edbc, chai n\u01b0\u1edbc, c\u1ed1c,&#8230; Khi n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay, h\u1ecdc sinh c\u00f3 th\u1ec3 t\u00ednh to\u00e1n th\u1ec3 t\u00edch c\u1ee7a c\u00e1c v\u1eadt th\u1ec3 n\u00e0y m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c.<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304902\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6.jpg\" alt=\"V\u00ec sao h\u1ecdc sinh c\u1ea7n ph\u1ea3i n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2><span style=\"font-weight: 400;\">T\u1ea7m quan tr\u1ecdng c\u1ee7a c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay trong h\u00ecnh h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Vi\u1ec7c v\u1eadn d\u1ee5ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay trong h\u00ecnh h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng r\u1ea5t quan tr\u1ecdng. B\u1edfi v\u00ec trong c\u00e1c ng\u00e0nh ngh\u1ec1 \u0111\u1ec1u y\u00eau c\u1ea7u c\u00e1c k\u1ef9 s\u01b0 c\u1ea7n ph\u1ea3i t\u00ednh to\u00e1n ch\u00ednh x\u00e1c \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3 th\u1ec3 t\u00edch V c\u1ee7a kh\u1ed1i tr\u00f2n xoay. <\/span><\/p>\n<h3>Trong h\u00ecnh h\u1ecdc kh\u00f4ng gian<\/h3>\n<p><span style=\"font-weight: 400;\">D\u01b0\u1edbi \u0111\u00e2y l\u00e0 t\u1ea7m quan tr\u1ecdng vi\u1ec7c \u00e1p d\u1ee5ng hi\u1ec7u qu\u1ea3 c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V kh\u1ed1i tr\u00f2n xoay trong h\u00ecnh h\u1ecdc kh\u00f4ng gian.\u00a0<\/span><\/p>\n<ul>\n<li>\u1ee8ng d\u1ee5ng ri\u00eang bi\u1ec7t trong ng\u00e0nh v\u1eadt l\u00fd, \u0111\u1eb7c bi\u1ec7t l\u00e0 c\u01a1 h\u1ecdc. V\u00ed d\u1ee5 khi c\u1ea7n ph\u1ea3i t\u00ednh \u0111\u01b0\u1ee3c kh\u1ed1i l\u01b0\u1ee3ng c\u1ee7a m\u1ed9t v\u1eadt th\u1ec3 \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh th\u00f4ng qua vi\u1ec7c quay xung quanh m\u1ed9t tr\u1ee5c. L\u00fac n\u00e0y ta c\u1ea7n ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c th\u00f4ng tin th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i v\u1eadt th\u1ec3 \u0111\u00f3 \u0111\u1ec3 t\u00ednh kh\u1ed1i l\u01b0\u1ee3ng.<\/li>\n<li>Trong tr\u01b0\u1eddng h\u1ee3p v\u1ec1 kh\u1ed1i tr\u00f2n xoay th\u00ec th\u1ec3 t\u00edch l\u00e0 thu\u1eadt ng\u1eef c\u1ef1c k\u1ef3 quan tr\u1ecdng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c ph\u1ea7n di\u1ec7n t\u00edch m\u1eb7t c\u1eaft v\u00e0 ph\u1ea7n di\u1ec7n t\u00edch c\u1ee7a b\u1ec1 m\u1eb7t c\u00f3 kh\u1ed1i h\u00ecnh d\u1ea1ng tr\u00f2n xoay.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304903\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7.jpg\" alt=\"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda - trong h\u00ecnh h\u1ecdc kh\u00f4ng gian\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h3>Trong cu\u1ed9c s\u1ed1ng<\/h3>\n<p><span style=\"font-weight: 400;\">D\u01b0\u1edbi \u0111\u00e2y l\u00e0 t\u1ea7m quan tr\u1ecdng vi\u1ec7c \u00e1p d\u1ee5ng hi\u1ec7u qu\u1ea3 c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch V kh\u1ed1i tr\u00f2n xoay trong cu\u1ed9c s\u1ed1ng.\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Vi\u1ec7c \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch gi\u00fap hi\u1ec3u r\u00f5 h\u01a1n \u0111\u01b0\u1ee3c v\u1ec1 t\u00ednh ch\u1ea5t v\u1ec1 h\u00ecnh h\u1ecdc c\u1ee7a kh\u1ed1i tr\u00f2n xoay. B\u00ean c\u1ea1nh \u0111\u00f3, ch\u00fang ta s\u1ebd n\u1eafm \u0111\u01b0\u1ee3c ph\u1ea7n v\u1ecb tr\u00ed v\u1edbi tr\u1ee5c quay, k\u00edch th\u01b0\u1edbc v\u00e0 \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a kh\u1ed1i tr\u00f2n xoay. \u0110\u00e2y l\u00e0 c\u00e1c y\u1ebfu t\u1ed1 r\u1ea5t quan tr\u1ecdng \u0111\u1ec3 \u00e1p d\u1ee5ng nh\u1eefng th\u00f4ng s\u1ed1 kh\u00e1c \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">D\u1ec5 d\u00e0ng \u00e1p d\u1ee5ng v\u00e0o c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf v\u1edbi c\u00e1c ng\u00e0nh ngh\u1ec1 kh\u00e1c nh\u01b0 k\u1ef9 thu\u1eadt, x\u00e2y d\u1ef1ng, ng\u00e0nh c\u00f4ng nghi\u1ec7p v\u00e0 thi\u1ebft k\u1ebf. Khi n\u1eafm v\u1eefng \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay th\u00ec s\u1ebd c\u00f3 th\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c ph\u1ea7n v\u1eadt li\u1ec7u c\u1ea7n s\u1eed d\u1ee5ng m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c, hi\u1ec7u qu\u1ea3.\u00a0<\/span><\/li>\n<li>Th\u1ec3 hi\u1ec7n \u0111\u01b0\u01a1c k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 khi \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay. Kh\u00f4ng ch\u1ec9 th\u1ec3 hi\u1ec7n v\u1ec1 m\u1eb7t ki\u1ebfn th\u1ee9c v\u1ec1 to\u00e1n h\u1ecdc m\u00e0 c\u00f2n cho th\u1ea5y \u0111\u01b0\u1ee3c kh\u1ea3 n\u0103ng t\u01b0 duy, gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 v\u00e0 t\u1ed5 ch\u1ee9c \u0111\u01b0\u1ee3c th\u00f4ng tin c\u1ee7a b\u1ea1n m\u1ed9t c\u00e1ch r\u00f5 r\u00e0ng.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304904\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8.jpg\" alt=\"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda - trong cu\u1ed9c s\u1ed1ng\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2><span style=\"font-weight: 400;\">Kh\u00f4ng d\u00f9ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay th\u00ec c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c kh\u00f4ng?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">N\u1ebfu kh\u00f4ng s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay th\u00ec c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c. Tuy nhi\u00ean, c\u00e1ch t\u00ednh s\u1ebd ph\u1ee9c t\u1ea1p h\u01a1n v\u00e0 \u0111\u00f2i h\u1ecfi nhi\u1ec1u b\u01b0\u1edbc h\u01a1n. C\u00e1ch t\u00ednh th\u1ec3 t\u00edch v\u1eadt th\u1ec3 tr\u00f2n xoay d\u1ef1a tr\u00ean nguy\u00ean l\u00fd t\u00edch ph\u00e2n. Th\u1ec3 t\u00edch c\u1ee7a v\u1eadt th\u1ec3 tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch chia nh\u1ecf v\u1eadt th\u1ec3 th\u00e0nh nhi\u1ec1u ph\u1ea7n nh\u1ecf, m\u1ed7i ph\u1ea7n l\u00e0 m\u1ed9t h\u00ecnh tr\u00f2n.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch c\u1ee7a m\u1ed7i ph\u1ea7n h\u00ecnh tr\u00f2n \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c \u03c0r\u00b2, trong \u0111\u00f3 r l\u00e0 b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh tr\u00f2n. Sau \u0111\u00f3, ta t\u00ednh t\u1ed5ng di\u1ec7n t\u00edch c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n h\u00ecnh tr\u00f2n n\u00e0y b\u1eb1ng c\u00e1ch t\u00ednh t\u00edch ph\u00e2n.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i n\u00f3n tr\u00f2n xoay, ta c\u00f3 th\u1ec3 chia kh\u1ed1i n\u00f3n th\u00e0nh nhi\u1ec1u ph\u1ea7n nh\u1ecf, m\u1ed7i ph\u1ea7n l\u00e0 m\u1ed9t h\u00ecnh n\u00f3n nh\u1ecf. Di\u1ec7n t\u00edch c\u1ee7a m\u1ed7i ph\u1ea7n h\u00ecnh n\u00f3n nh\u1ecf \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c <strong>\u03c0r\u00b2h\/3<\/strong>, trong \u0111\u00f3 r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y c\u1ee7a h\u00ecnh n\u00f3n nh\u1ecf, h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh n\u00f3n nh\u1ecf. Sau \u0111\u00f3, ta t\u00ednh t\u1ed5ng di\u1ec7n t\u00edch c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n h\u00ecnh n\u00f3n n\u00e0y b\u1eb1ng c\u00e1ch t\u00ednh t\u00edch ph\u00e2n.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304905\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9.jpg\" alt=\"Kh\u00f4ng d\u00f9ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay th\u00ec c\u00f3 th\u1ec3 t\u00ednh\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00edch ph\u00e2n t\u00ednh di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh tr\u00f2n nh\u1ecf l\u00e0: S = \u03c0\u222b[a,b] (f(x))^2 dx. Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 di\u1ec7n t\u00edch c\u1ee7a h\u00ecnh tr\u00f2n nh\u1ecf<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">f(x) \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a h\u00e0m s\u1ed1 gi\u1edbi h\u1ea1n mi\u1ec1n D c\u1ee7a v\u1eadt th\u1ec3 tr\u00f2n xoay<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">a v\u00e0 b \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a\u00a0 l\u00e0 hai \u0111i\u1ec3m gi\u1edbi h\u1ea1n c\u1ee7a mi\u1ec1n D<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong l\u0129nh v\u1ef1c n\u00e0o?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u0110\u1ed1i v\u1edbi c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong r\u1ea5t nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau trong cu\u1ed9c s\u1ed1ng nh\u01b0:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">L\u0129nh v\u1ef1c to\u00e1n h\u1ecdc: \u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng b\u00e0i to\u00e1n c\u1ef1c k\u1ef3 c\u01a1 b\u1ea3n c\u00f3 trong ph\u1ea7n h\u00ecnh h\u1ecdc kh\u00f4ng gian l\u1edbp 12. \u0110\u1ed1i t\u01b0\u1ee3ng b\u00e0i to\u00e1n n\u00e0y \u0111\u00f3 ch\u00ednh l\u00e0 kh\u1ed1i tr\u00f2n \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1edfi vi\u1ec7c quay quanh \u0111\u01b0\u1eddng cong \u0111\u00e3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh. D\u1ea1ng to\u00e1n n\u00e0y y\u00eau c\u1ea7u h\u1ecdc sinh ph\u1ea3i n\u1eafm v\u1eefng \u0111\u01b0\u1ee3c ki\u1ebfn th\u1ee9c v\u1ec1 ph\u1ea7n di\u1ec7n t\u00edch S v\u00e0 th\u1ec3 t\u00edch V c\u1ee7a kh\u1ed1i c\u1ea7u, h\u00ecnh tr\u1ee5 hay nh\u1eefng h\u00ecnh kh\u00e1c \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi \u0111\u01b0\u1eddng cong.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">L\u0129nh v\u1ef1c k\u1ef9 thu\u1eadt: Trong l\u0129nh v\u1ef1c n\u00e0y vi\u1ec7c t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch tr\u00f2n xoay r\u1ea5t c\u1ea7n thi\u1ebft. C\u1ee5 th\u1ec3 nh\u01b0 thi\u1ebft k\u1ebf c\u00e1c h\u1ec7 th\u1ed1ng \u0111\u01b0\u1eddng \u1ed1ng th\u00ec c\u1ea7n t\u00ednh \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c ph\u1ea7n th\u1ec3 t\u00edch c\u1ee7a \u1ed1ng \u0111\u1ec3 c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh ch\u00ednh x\u00e1c ph\u1ea7n dung t\u00edch ch\u1ee9a ch\u1ea5t c\u1ea7n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304894\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10.jpg\" alt=\"C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong l\u0129nh v\u1ef1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p><span style=\"font-weight: 400;\">L\u0129nh v\u1ef1c x\u00e2y d\u1ef1ng: trong l\u0129nh v\u1ef1c n\u00e0y ph\u1ea7n th\u1ec3 t\u00edch V c\u1ee7a kh\u1ed1i tr\u00f2n xoay th\u01b0\u1eddng \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ednh to\u00e1n ch\u00ednh x\u00e1c c\u00e1c c\u00f4ng tr\u00ecnh c\u00f3 h\u00ecnh d\u1ea1ng tron xoay. V\u00ed d\u1ee5 nh\u01b0 c\u00e1c c\u1ed9t xi m\u0103ng, ao h\u1ed3, h\u1ed3 \u0111\u1ea5t. \u0110\u1ec3 c\u00f3 th\u1ec3 ti\u1ebfn h\u00e0nh x\u00e2y d\u1ef1ng ch\u00ednh x\u00e1c th\u00ec c\u1ea7n ph\u1ea3i t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch V c\u1ee7a kh\u1ed1i tr\u00f2n xoay,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">L\u0129nh v\u1ef1c thi\u1ebft k\u1ebf s\u1ea3n ph\u1ea9m: \u0110\u1ed1i v\u1edbi l\u0129nh v\u1ef1c n\u00e0y, khi t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch v\u1eadt tr\u00f2n xoay s\u1ebd x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c ph\u1ea7n dung t\u00edch m\u1ed9t s\u1ed1 s\u1ea3n ph\u1ea9m c\u00f3 h\u00ecnh d\u1ea1ng tr\u00f2n xoay nh\u01b0 \u1ed1ng h\u00fat, h\u0169, l\u1ecd, v\u00f2ng bi,&#8230;\u00a0<\/span><\/p>\n<h2>T\u1ed5ng k\u1ebft<\/h2>\n<p>Th\u00f4ng qua b\u00e0i vi\u1ebft tr\u00ean, Ho\u00e0ng H\u00e0 Mobile \u0111\u00e3 gi\u00fap b\u1ea1n n\u1eafm \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay m\u1ed9t c\u00e1ch chi ti\u1ebft. B\u00ean c\u1ea1nh \u0111\u00f3, b\u1ea1n c\u00f3 th\u1ec3 n\u1eafm \u0111\u01b0\u1ee3c t\u1ea7m quan tr\u1ecdng c\u1ee7a c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh h\u1ecdc kh\u1ed1i tr\u00f2n xoay v\u00e0 vi\u1ec7c \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c n\u00e0y trong c\u00e1ch l\u0129nh v\u1ef1c th\u1ef1c t\u1ebf nh\u01b0 th\u1ebf n\u00e0o.<\/p>\n<p>Xem th\u00eam:<\/p>\n<ul>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/bang-don-vi-do-khoi-luong\/\">B\u1ea3ng \u0111\u01a1n v\u1ecb \u0111o kh\u1ed1i l\u01b0\u1ee3ng chi ti\u1ebft nh\u1ea5t \u2013 C\u00e1ch ghi nh\u1edb v\u00e0 quy \u0111\u1ed5i ch\u00fang<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-huu-ti-la-gi\/\">S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng c\u1ee7a c\u00e1c s\u1ed1 trong To\u00e1n h\u1ecdc<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay l\u00e0 m\u1ed9t trong nh\u1eefng \u0111\u1ec1 b\u00e0i to\u00e1n h\u1ecdc c\u1ef1c k\u1ef3 th\u00fa v\u1ecb \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong h\u00ecnh h\u1ecdc kh\u00f4ng gian c\u1ea5p b\u1eadc trung h\u1ecdc. Nh\u1edd v\u00e0o c\u00f4ng th\u1ee9c ch\u00fang ta c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch v\u1eadt th\u1ec3 kh\u1ed1i tr\u00f2n xoay quanh tr\u1ee5c Oy v\u00e0 Ox. Th\u00f4ng [&hellip;]<\/p>\n","protected":false},"author":91,"featured_media":304891,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay","_yoast_wpseo_title":"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda","_yoast_wpseo_metadesc":"C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay c\u1ef1c k\u1ef3 quan tr\u1ecdng \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau to\u00e1n h\u1ecdc, x\u00e2y d\u1ef1ng, thi\u1ebft k\u1ebf.","footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-304886","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 v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda<\/title>\n<meta name=\"description\" content=\"C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u1ed1i tr\u00f2n xoay c\u1ef1c k\u1ef3 quan tr\u1ecdng \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau to\u00e1n h\u1ecdc, x\u00e2y d\u1ef1ng, thi\u1ebft k\u1ebf.\" \/>\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\/cong-thuc-the-tich-khoi-tron-xoay\/\" \/>\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 kh\u1ed1i tr\u00f2n xoay v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda\" \/>\n<meta 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