{"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":"2024-01-12T19:56:50","modified_gmt":"2024-01-12T12:56:50","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><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-304895 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-1.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-1\" 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\"><\/picture><\/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><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-304896 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-2.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-2\" 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\"><\/picture><\/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\u00ea\u0309u ki\u00ea\u0323n c\u00e2\u0300n \u0111\u00ea\u0309 a\u0301p du\u0323ng c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u0110\u00ea\u0309 co\u0301 th\u00ea\u0309 a\u0301p du\u0323ng \u0111\u01b0\u01a1\u0323c c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay \u0111\u01b0\u01a1\u0323c n\u00eau tr\u00ean c\u00e2\u0300n pha\u0309i \u0111a\u0301p \u01b0\u0301ng \u0111i\u00ea\u0300u ki\u00ea\u0323n c\u00e2\u0300n trong toa\u0301n ho\u0323c. \u0110i\u00ea\u0300u ki\u00ea\u0323n c\u00e2\u0300n \u0111o\u0301 la\u0300 kh\u00f4\u0301i tro\u0300n xoay \u0111\u01b0\u01a1\u0323c ta\u0323o ra th\u00f4ng qua vi\u00ea\u0323c quay xung quanh m\u00f4\u0323t tru\u0323c c\u00f4\u0301 \u0111i\u0323nh. Co\u0301 nghi\u0303a ph\u00e2\u0300n v\u00e2\u0323t th\u00ea\u0309 na\u0300y se\u0303 \u0111\u01b0\u01a1\u0323c m\u00f4\u0323t \u0111\u01b0\u01a1\u0300ng cong c\u00f4\u0301 \u0111i\u0323nh va\u0300 xoay xung quanh tru\u0323c nh\u00e2\u0301t \u0111i\u0323nh \u0111\u00ea\u0309 ta\u0323o ra hi\u0300nh da\u0323ng v\u00e2\u0323t th\u00ea\u0309 tro\u0300n xoay. Cu\u0323 th\u00ea\u0309, \u0111\u00ea\u0309 a\u0301p du\u0323ng \u0111\u01b0\u01a1\u0323c kh\u00f4\u0301i tro\u0300n xoay thi\u0300 c\u00e2\u0300n pha\u0309i \u0111a\u0301p \u01b0\u0301ng \u0111\u01b0\u01a1\u0323c \u0111\u00e2\u0300y \u0111u\u0309 ca\u0301c th\u00f4ng tin sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u01b0\u01a1\u0300ng cong xa\u0301c \u0111i\u0323nh c\u00f4\u0301 \u0111i\u0323nh \u0111\u01b0\u01a1\u0323c kh\u00f4\u0301i v\u00e2\u0323t th\u00ea\u0309: Ph\u00e2\u0300n \u0111\u01b0\u01a1\u0300ng cong na\u0300y se\u0303 \u0111\u01b0\u01a1\u0323c xa\u0301c \u0111i\u0323nh th\u00f4ng qua m\u00f4\u0323t ha\u0309m s\u00f4\u0301 bi\u00ea\u0309u di\u00ea\u0303n \u0111o\u0301 la\u0300 y= f(x) hay x= g(y). Trong \u0111o\u0301 f(x) va\u0300 g)y) \u0111\u01b0\u01a1\u0323c \u0111i\u0323nh nghi\u0303a la\u0300 ph\u01b0\u01a1ng tri\u0300nh ha\u0300m s\u00f4\u0301 li\u00ean tru\u0323c n\u0103\u0300m trong \u0111oa\u0323n khoa\u0309ng ca\u0301ch [a,b] v\u01a1\u0301i \u0111i\u00ea\u0300u ki\u00ea\u0323n a &lt; b.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110oa\u0323n [a,b] la\u0300 khoa\u0309ng ca\u0301ch pha\u0323m vi c\u00e2\u0300n \u0111\u01b0\u01a1\u0323c xa\u0301c \u0111i\u0323nh co\u0301 trong ha\u0300m s\u00f4\u0301 cu\u0309a c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch V.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Tru\u0323c quanh Ox ho\u0103\u0323c Oy la\u0300 ky\u0301 hi\u00ea\u0323u \u0111a\u0323i di\u00ea\u0323n bi\u00ea\u0309u di\u00ea\u0303n cho ca\u0301c tru\u0323c c\u00f4\u0301 \u0111i\u0323nh \u0111\u01b0\u01a1\u0323c kh\u00f4\u0301i tro\u0300n quay xung quanh.\u00a0<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-304897 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-3.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-3\" 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\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Nhi\u0300n chung, \u0111\u00ea\u0309 co\u0301 th\u00ea\u0309 ti\u0301nh \u0111\u01b0\u01a1\u0323c th\u00ea\u0309 ti\u0301ch V cu\u0309a kh\u00f4\u0301i tro\u0300n xoay thi\u0300 ba\u0323n c\u00e2\u0300n pha\u0309i xa\u0301c \u0111i\u0323nh ph\u00e2\u0300n \u0111\u01b0\u01a1\u0300ng cong \u0111\u01b0\u01a1\u0323c \u0111i\u0323nh hi\u0300nh cu\u0309a kh\u00f4\u0301i tro\u0300n. Cu\u0300ng v\u01a1\u0301i ph\u00e2\u0300n pha\u0323m vi xa\u0301c \u0111i\u0323nh bao g\u00f4\u0300m tru\u0323c c\u00f4\u0301 \u0111i\u0323nh va\u0300 \u0111\u01b0\u01a1\u0300ng cong kh\u00f4\u0301i tro\u0300n quay xung quanh. Cu\u00f4\u0301i cu\u0300ng, a\u0301p du\u0323ng \u0111\u01b0\u01a1\u0323c c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay d\u01b0\u0323a va\u0300o ha\u0300m s\u00f4\u0301 \u0111\u01b0\u01a1\u0300ng xong cu\u0300ng pha\u0323m vi \u0111a\u0303 \u0111\u01b0\u01a1\u0323c xa\u0301c \u0111i\u0323nh \u0111\u00ea\u0309 ti\u0301nh \u0111\u01b0\u01a1\u0323c th\u00ea\u0309 ti\u0301ch V theo \u0111\u00ea\u0300 ba\u0300i.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay \u0111\u01b0\u01a1\u0323c ti\u0301nh theo c\u00f4ng th\u01b0\u0301c na\u0300o kha\u0301c?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Ngoa\u0300i c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay \u0111\u01b0\u01a1\u0323c n\u00eau tr\u00ean, v\u00e2\u0323t th\u00ea\u0309 tro\u0300n xoay co\u0300n \u0111\u01b0\u01a1\u0323c ti\u0301nh d\u01b0\u0323a theo c\u00f4ng th\u01b0\u0301c kha\u0301c. \u0110\u00e2\u0300u ti\u00ean, c\u00e2\u0300n pha\u0309i xa\u0301c \u0111i\u0323nh \u0111\u01b0\u01a1\u0323c mi\u00ea\u0300n (D) ma\u0300 v\u00e2\u0323t th\u00ea\u0309 xoay xung quanh. Khu v\u01b0\u0323c mi\u00ea\u0300n na\u0300y se\u0303 \u0111\u01b0\u01a1\u0323c gi\u01a1\u0301i ha\u0323n b\u01a1\u0309i ph\u00e2\u0300n \u0111\u00f4\u0300 thi\u0300 bi\u00ea\u0309u di\u00ea\u0303n b\u01a1\u0309i ph\u01b0\u01a1ng tri\u0300nh ha\u0300m s\u00f4\u0301 y= f(x), v\u01a1\u0301i \u0111oa\u0323n th\u0103\u0309ng ha\u0300m s\u00f4\u0301 x=a, x=b va\u0300 xoay xung quanh tru\u0323c Ox.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ti\u00ea\u0301p theo, ti\u00ea\u0301n ha\u0300nh ti\u0301nh di\u00ea\u0323n ti\u0301ch S \u0111\u01b0\u01a1\u0323c quay xung quanh tru\u0323c Ox cu\u0309a ph\u00e2\u0300n di\u00ea\u0323n ti\u0301ch gi\u01a1\u0301i ha\u0323n D v\u01a1\u0301i c\u00f4ng th\u01b0\u0301c \u0111o\u0301 la\u0300 <\/span><span style=\"font-weight: 400;\">S = \u222b[a,b] (\u03c0[f(x)]^2)dx. Cu\u00f4\u0301i cu\u0300ng ti\u00ea\u0301n ha\u0300nh ti\u0301nh th\u00ea\u0309 ti\u0301ch V kh\u00f4\u0301i tro\u0300n xoay b\u0103\u0300ng ca\u0301ch l\u00e2\u0301y di\u00ea\u0323n ti\u0301ch \u0111a\u0303 ti\u0301nh \u0111\u01b0\u01a1\u0323c nh\u00e2n v\u01a1\u0301i chi\u00ea\u0300u da\u0300i L vo\u0300ng quanh tru\u0323c Ox.\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304899 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-4.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-4\" 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\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Do \u0111o\u0301, c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay se\u0303 \u0111\u01b0\u01a1\u0323c ti\u0301nh theo c\u00f4ng th\u01b0\u0301c kha\u0301c \u0111o\u0301 la\u0300: <\/span><b>V= S * L<\/b><span style=\"font-weight: 400;\">. <\/span><span style=\"font-weight: 400;\">Khi a\u0301p du\u0323ng c\u00f4ng th\u01b0\u0301c na\u0300y thi\u0300 ba\u0323n se\u0303 ti\u0301nh \u0111\u01b0\u01a1\u0323c th\u00ea\u0309 ti\u0301ch v\u01a1\u0301i v\u00e2\u0323t th\u00ea\u0309 kh\u00f4\u0301i tro\u0300n xoay m\u00f4\u0323t ca\u0301ch chi\u0301nh xa\u0301c va\u0300 \u0111\u01a1n gia\u0309n h\u01a1n.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">H\u01b0\u01a1\u0301ng d\u00e2\u0303n ti\u0301nh th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay chi ti\u00ea\u0301t\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau khi bi\u00ea\u0301t \u0111\u01b0\u01a1\u0323c c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay nh\u01b0ng nhi\u00ea\u0300u ba\u0323n ch\u01b0a n\u0103\u0301m \u0111\u01b0\u01a1\u0323c ngu\u00f4\u0300n g\u00f4\u0301c ca\u0301c b\u01b0\u01a1\u0301c chi ti\u00ea\u0301t ti\u0301nh th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay. D\u01b0\u01a1\u0301i \u0111\u00e2y la\u0300 ca\u0301c b\u01b0\u01a1\u0301c h\u01b0\u01a1\u0301ng d\u00e2\u0303n chi ti\u00ea\u0301t ti\u0301nh th\u00ea\u0309 ti\u0301ch v\u00e2\u0323t th\u00ea\u0309 tro\u0300n xoay nh\u01b0 sau:\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u01a1\u0301c 1: \u0110\u00e2\u0300u ti\u00ean, c\u00e2\u0300n xa\u0301c \u0111i\u0323nh \u0111\u01b0\u01a1\u0323c khu v\u01b0\u0323c mi\u00ea\u0300n gi\u01a1\u0301i ha\u0323n cu\u0309a v\u00e2\u0323t th\u00ea\u0309 b\u01a1\u0309i ph\u01b0\u01a1ng tri\u0300nh bi\u00ea\u0309u di\u00ea\u0303n ha\u0300m s\u00f4\u0301 ho\u0103\u0323c \u0111\u01b0\u01a1\u0300ng cong \u0111\u01b0\u01a1\u0323c v\u00e2\u0323t th\u00ea\u0309 quay xung quanh.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u01a1\u0301c 2: Ti\u00ea\u0301p theo, xa\u0301c \u0111i\u0323nh ph\u00e2\u0300n \u0111oa\u0323n th\u0103\u0309ng tru\u0323c Ox \u0111\u01b0\u01a1\u0323c kh\u00f4\u0301i tro\u0300n quay xung quanh. Tru\u0323c Ox la\u0300 tru\u0323c \u0111\u00f4\u0301i x\u01b0\u0301ng cu\u0309a kh\u00f4\u0301i tro\u0300n.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u01a1\u0301c 3: Sau \u0111o\u0301, ti\u00ea\u0301n ha\u0300nh ti\u0301nh di\u00ea\u0323n ti\u0301ch S ph\u00e2\u0300n mi\u00ea\u0300n gi\u01a1\u0301i ha\u0323n \u0111\u01b0\u01a1\u0323c quay xung quanh tru\u0323c Ox, \u0111\u00e2y la\u0300 ph\u00e2\u0300n di\u00ea\u0323n ti\u0301ch \u0111\u01b0\u01a1\u0323c ta\u0323o ra b\u01a1\u0309i mi\u00ea\u0300n gi\u01a1\u0301i ha\u0323n khi quay xung quanh tru\u0323c Ox.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u01a1\u0301c 4: Ti\u00ea\u0301p theo, a\u0301p du\u0323ng c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch V kh\u00f4\u0301i tro\u0300n xoay <\/span><span style=\"font-weight: 400;\">V = \u03c0\u222b(S)dx. Trong \u0111o\u0301, \u03c0 \u0111\u01b0\u01a1\u0323c \u0111i\u0323nh nghi\u0303a la\u0300 s\u00f4\u0301 Pi co\u0301 gia\u0301 tri\u0323 x\u00e2\u0301p xi\u0309 3.14 va\u0300 \u222b(S)dx la\u0300 c\u00f4ng th\u01b0\u0301c ti\u0301ch ph\u00e2n \u0111\u01b0\u01a1\u0323c xa\u0301c \u0111i\u0323nh ph\u00e2\u0300n di\u00ea\u0323n ti\u0301ch S quanh xung quanh tru\u0323c X.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u01b0\u01a1\u0301c 5: Cu\u00f4\u0301i cu\u0300ng th\u01b0\u0323c hi\u00ea\u0323n phe\u0301p ti\u0301nh ti\u0301nh ph\u00e2n \u0111\u00ea\u0309 co\u0301 th\u00ea\u0309 xa\u0301c \u0111i\u0323nh ph\u00e2\u0300n gia\u0301 tri\u0323 th\u00ea\u0309 ti\u0301ch V cu\u0309a kh\u00f4\u0301i tro\u0300n xoay.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304901 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-5.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-5\" 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\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Th\u00f4ng qua ca\u0301c b\u01b0\u01a1\u0301c tr\u00ean ta co\u0301 th\u00ea\u0309 ti\u0301nh \u0111\u01b0\u01a1\u0323c toa\u0300n b\u00f4\u0323 th\u00ea\u0309 ti\u0301ch cu\u0309a kh\u00f4\u0301i tro\u0300n xoay c\u00e2\u0300n ti\u0301nh.\u00a0<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">Vi\u0300 sao ho\u0323c sinh c\u00e2\u0300n pha\u0309i n\u0103\u0301m ro\u0303 c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n 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 ti\u0301nh 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 ti\u0301nh 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 ti\u0301nh 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><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304902 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-6.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-6\" 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\"><\/picture><\/p>\n<h2><span style=\"font-weight: 400;\">T\u00e2\u0300m quan tro\u0323ng cu\u0309a c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay trong h\u00ecnh h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Vi\u00ea\u0323c v\u00e2\u0323n du\u0323ng c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay trong h\u00ecnh h\u1ecdc v\u00e0 cu\u00f4\u0323c s\u00f4\u0301ng r\u00e2\u0301t quan tro\u0323ng. B\u01a1\u0309i vi\u0300 trong ca\u0301c nga\u0300nh ngh\u00ea\u0300 \u0111\u00ea\u0300u y\u00eau c\u00e2\u0300u ca\u0301c ky\u0303 s\u01b0 c\u00e2\u0300n pha\u0309i ti\u0301nh toa\u0301n chi\u0301nh xa\u0301c \u0111\u01b0\u01a1\u0323c hi\u00ea\u0323u qua\u0309 th\u00ea\u0309 ti\u0301ch V cu\u0309a kh\u00f4\u0301i tro\u0300n xoay. <\/span><\/p>\n<h3>Trong h\u00ecnh h\u1ecdc kh\u00f4ng gian<\/h3>\n<p><span style=\"font-weight: 400;\">D\u01b0\u01a1\u0301i \u0111\u00e2y la\u0300 t\u00e2\u0300m quan tro\u0323ng vi\u00ea\u0323c a\u0301p du\u0323ng hi\u00ea\u0323u qua\u0309 c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch V kh\u00f4\u0301i tro\u0300n 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><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304903 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-7.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-7\" 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\"><\/picture><\/p>\n<h3>Trong cu\u1ed9c s\u1ed1ng<\/h3>\n<p><span style=\"font-weight: 400;\">D\u01b0\u01a1\u0301i \u0111\u00e2y la\u0300 t\u00e2\u0300m quan tro\u0323ng vi\u00ea\u0323c a\u0301p du\u0323ng hi\u00ea\u0323u qua\u0309 c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch V kh\u00f4\u0301i tro\u0300n xoay trong cu\u00f4\u0323c s\u00f4\u0301ng.\u00a0<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Vi\u00ea\u0323c a\u0301p du\u0323ng c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch giu\u0301p hi\u00ea\u0309u ro\u0303 h\u01a1n \u0111\u01b0\u01a1\u0323c v\u00ea\u0300 ti\u0301nh ch\u00e2\u0301t v\u00ea\u0300 hi\u0300nh ho\u0323c cu\u0309a kh\u00f4\u0301i tro\u0300n xoay. B\u00ean ca\u0323nh \u0111o\u0301, chu\u0301ng ta se\u0303 n\u0103\u0301m \u0111\u01b0\u01a1\u0323c ph\u00e2\u0300n vi\u0323 tri\u0301 v\u01a1\u0301i tru\u0323c quay, ki\u0301ch th\u01b0\u01a1\u0301c va\u0300 \u0111\u0103\u0323c \u0111i\u00ea\u0309m cu\u0309a kh\u00f4\u0301i tro\u0300n xoay. \u0110\u00e2y la\u0300 ca\u0301c y\u00ea\u0301u t\u00f4\u0301 r\u00e2\u0301t quan tro\u0323ng \u0111\u00ea\u0309 a\u0301p du\u0323ng nh\u01b0\u0303ng th\u00f4ng s\u00f4\u0301 kha\u0301c \u0111\u00ea\u0309 ti\u0301nh th\u00ea\u0309 ti\u0301ch v\u00e2\u0323t th\u00ea\u0309.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">D\u00ea\u0303 da\u0300ng a\u0301p du\u0323ng va\u0300o ca\u0301c ba\u0300i toa\u0301n th\u01b0\u0323c t\u00ea\u0301 v\u01a1\u0301i ca\u0301c nga\u0300nh ngh\u00ea\u0300 kha\u0301c nh\u01b0 ky\u0303 thu\u00e2\u0323t, x\u00e2y d\u01b0\u0323ng, nga\u0300nh c\u00f4ng nghi\u00ea\u0323p va\u0300 thi\u00ea\u0301t k\u00ea\u0301. Khi n\u0103\u0301m v\u01b0\u0303ng \u0111\u01b0\u01a1\u0323c c\u00f4ng th\u01b0\u0301c ti\u0301nh th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay thi\u0300 se\u0303 co\u0301 th\u00ea\u0309 ti\u0301nh toa\u0301n \u0111\u01b0\u01a1\u0323c ph\u00e2\u0300n v\u00e2\u0323t li\u00ea\u0323u c\u00e2\u0300n s\u01b0\u0309 du\u0323ng m\u00f4\u0323t ca\u0301ch chi\u0301nh xa\u0301c, hi\u00ea\u0323u qua\u0309.\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><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304904 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-8.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-8\" 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\"><\/picture><\/p>\n<h2><span style=\"font-weight: 400;\">Kh\u00f4ng du\u0300ng c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay thi\u0300 co\u0301 th\u00ea\u0309 ti\u0301nh \u0111\u01b0\u01a1\u0323c kh\u00f4ng?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">N\u00ea\u0301u kh\u00f4ng s\u01b0\u0309 du\u0323ng c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay thi\u0300 co\u0301 th\u00ea\u0309 ti\u0301nh \u0111\u01b0\u01a1\u0323c. 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><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304905 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-9.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-9\" 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\"><\/picture><\/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\u01a1\u0323c \u0111i\u0323nh nghi\u0303a la\u0300 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\u01a1\u0323c \u0111i\u0323nh nghi\u0303a 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\u01a1\u0323c \u0111i\u0323nh nghi\u0303a\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\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay \u0111\u01b0\u01a1\u0323c a\u0301p du\u0323ng trong li\u0303nh v\u01b0\u0323c na\u0300o?\u00a0<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u0110\u00f4\u0301i v\u01a1\u0301i c\u00f4ng th\u01b0\u0301c th\u00ea\u0309 ti\u0301ch kh\u00f4\u0301i tro\u0300n xoay \u0111\u01b0\u01a1\u0323c a\u0301p du\u0323ng trong r\u00e2\u0301t nhi\u00ea\u0300u li\u0303nh v\u01b0\u0323c kha\u0301c nhau trong cu\u00f4\u0323c s\u00f4\u0301ng nh\u01b0:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Li\u0303nh v\u01b0\u0323c toa\u0301n ho\u0323c: \u0110\u00e2y la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng ba\u0300i toa\u0301n c\u01b0\u0323c ky\u0300 c\u01a1 ba\u0309n co\u0301 trong ph\u00e2\u0300n hi\u0300nh ho\u0323c kh\u00f4ng gian l\u01a1\u0301p 12. \u0110\u00f4\u0301i t\u01b0\u01a1\u0323ng ba\u0300i toa\u0301n na\u0300y \u0111o\u0301 chi\u0301nh la\u0300 kh\u00f4\u0301i tro\u0300n \u0111\u01b0\u01a1\u0323c ta\u0323o tha\u0300nh b\u01a1\u0309i vi\u00ea\u0323c quay quanh \u0111\u01b0\u01a1\u0300ng cong \u0111a\u0303 \u0111\u01b0\u01a1\u0323c xa\u0301c \u0111i\u0323nh. Da\u0323ng toa\u0301n na\u0300y y\u00eau c\u00e2\u0300u ho\u0323c sinh pha\u0309i n\u0103\u0301m v\u01b0\u0303ng \u0111\u01b0\u01a1\u0323c ki\u00ea\u0301n th\u01b0\u0301c v\u00ea\u0300 ph\u00e2\u0300n di\u00ea\u0323n ti\u0301ch S va\u0300 th\u00ea\u0309 ti\u0301ch V cu\u0309a kh\u00f4\u0301i c\u00e2\u0300u, hi\u0300nh tru\u0323 hay nh\u01b0\u0303ng hi\u0300nh kha\u0301c \u0111\u01b0\u01a1\u0323c bi\u00ea\u0309u di\u00ea\u0303n b\u01a1\u0309i \u0111\u01b0\u01a1\u0300ng cong.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Li\u0303nh v\u01b0\u0323c ky\u0303 thu\u00e2\u0323t: Trong li\u0303nh v\u01b0\u0323c na\u0300y vi\u00ea\u0323c ti\u0301nh \u0111\u01b0\u01a1\u0323c th\u00ea\u0309 ti\u0301ch tro\u0300n xoay r\u00e2\u0301t c\u00e2\u0300n thi\u00ea\u0301t. Cu\u0323 th\u00ea\u0309 nh\u01b0 thi\u00ea\u0301t k\u00ea\u0301 ca\u0301c h\u00ea\u0323 th\u00f4\u0301ng \u0111\u01b0\u01a1\u0300ng \u00f4\u0301ng thi\u0300 c\u00e2\u0300n ti\u0301nh \u0111\u01b0\u01a1\u0323c chi\u0301nh xa\u0301c ph\u00e2\u0300n th\u00ea\u0309 ti\u0301ch cu\u0309a \u00f4\u0301ng \u0111\u00ea\u0309 co\u0301 th\u00ea\u0309 xa\u0301c \u0111i\u0323nh chi\u0301nh xa\u0301c ph\u00e2\u0300n dung ti\u0301ch ch\u01b0\u0301a ch\u00e2\u0301t c\u00e2\u0300n \u0111\u01b0\u01a1\u0323c s\u01b0\u0309 du\u0323ng.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-304894 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/01\/cong-thuc-the-tich-khoi-tron-xoay-10.jpg\" alt=\"cong-thuc-the-tich-khoi-tron-xoay-10\" 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\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Li\u0303nh v\u01b0\u0323c x\u00e2y d\u01b0\u0323ng: trong li\u0303nh v\u01b0\u0323c na\u0300y ph\u00e2\u0300n th\u00ea\u0309 ti\u0301ch V cu\u0309a kh\u00f4\u0301i tro\u0300n xoay th\u01b0\u01a1\u0300ng \u0111\u01b0\u01a1\u0323c du\u0300ng \u0111\u00ea\u0309 co\u0301 th\u00ea\u0309 ti\u0301nh toa\u0301n chi\u0301nh xa\u0301c ca\u0301c c\u00f4ng tri\u0300nh co\u0301 hi\u0300nh da\u0323ng tron xoay. Vi\u0301 du\u0323 nh\u01b0 ca\u0301c c\u00f4\u0323t xi m\u0103ng, ao h\u00f4\u0300, h\u00f4\u0300 \u0111\u00e2\u0301t. \u0110\u00ea\u0309 co\u0301 th\u00ea\u0309 ti\u00ea\u0301n ha\u0300nh x\u00e2y d\u01b0\u0323ng chi\u0301nh xa\u0301c thi\u0300 c\u00e2\u0300n pha\u0309i ti\u0301nh \u0111\u01b0\u01a1\u0323c th\u00ea\u0309 ti\u0301ch V cu\u0309a kh\u00f4\u0301i tro\u0300n xoay,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Li\u0303nh v\u01b0\u0323c thi\u00ea\u0301t k\u00ea\u0301 sa\u0309n ph\u00e2\u0309m: \u0110\u00f4\u0301i v\u01a1\u0301i li\u0303nh v\u01b0\u0323c na\u0300y, khi ti\u0301nh \u0111\u01b0\u01a1\u0323c th\u00ea\u0309 ti\u0301ch v\u00e2\u0323t tro\u0300n xoay se\u0303 xa\u0301c \u0111i\u0323nh \u0111\u01b0\u01a1\u0323c ph\u00e2\u0300n dung ti\u0301ch m\u00f4\u0323t s\u00f4\u0301 sa\u0309n ph\u00e2\u0309m co\u0301 hi\u0300nh da\u0323ng tro\u0300n xoay nh\u01b0 \u00f4\u0301ng hu\u0301t, hu\u0303, lo\u0323, vo\u0300ng 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":{"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 v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\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\" 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