{"id":298894,"date":"2023-12-25T16:29:48","date_gmt":"2023-12-25T09:29:48","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=298894"},"modified":"2025-12-20T14:53:09","modified_gmt":"2025-12-20T07:53:09","slug":"dien-tich-xung-quanh-hinh-non","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-xung-quanh-hinh-non\/","title":{"rendered":"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n: Sxq = \u03c0.r.l (Chi ti\u1ebft &#038; v\u00ed d\u1ee5)"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n (Sxq = \u03c0.r.l) l\u00e0 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n To\u00e1n 9, \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh t\u1eeb vi\u1ec7c quay tam gi\u00e1c vu\u00f4ng quanh c\u1ea1nh g\u00f3c vu\u00f4ng. B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn chi ti\u1ebft c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n (Stp = \u03c0.r.l + \u03c0.r\u00b2), th\u1ec3 t\u00edch (V = 1\/3 \u03c0.r\u00b2.h) k\u00e8m v\u00ed d\u1ee5 minh h\u1ecda, b\u00e0i t\u1eadp SGK v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf t\u1eeb Ho\u00e0ng H\u00e0 Mobile.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">H\u00ecnh n\u00f3n l\u00e0 g\u00ec?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Trong to\u00e1n h\u1ecdc, h\u00ecnh n\u00f3n l\u00e0 m\u1ed9t \u0111\u1ed1i t\u01b0\u1ee3ng h\u00ecnh h\u1ecdc kh\u00f4ng gian c\u00f3 d\u1ea1ng gi\u1ed1ng nh\u01b0 m\u1ed9t chi\u1ebfc n\u00f3n th\u1ef1c t\u1ebf. \u0110i\u1ec3m \u0111\u1eb7c bi\u1ec7t c\u1ee7a lo\u1ea1i h\u00ecnh h\u1ecdc n\u00e0y \u0111\u00f3 l\u00e0 ch\u00fang \u0111\u01b0\u1ee3c c\u1ea5u t\u1ea1o v\u1edbi m\u1ed9t \u0111\u1ec9nh nh\u1ecdn v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n \u1edf \u0111\u00e1y d\u1ef1a tr\u00ean g\u00f3c nh\u00ecn 3 chi\u1ec1u \u0111\u1eb7c bi\u1ec7t. Trong \u0111\u00f3, h\u00ecnh n\u00f3n th\u01b0\u1eddng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi ba y\u1ebfu t\u1ed1 ch\u00ednh g\u1ed3m b\u00e1n k\u00ednh c\u1ee7a \u0111\u00e1y (\u0111\u01b0\u1eddng tr\u00f2n \u1edf \u0111\u00e1y), chi\u1ec1u cao v\u00e0 \u0111\u1ec9nh.\u00a0<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298896 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-1.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Theo \u0111\u00f3, c\u00e1c y\u1ebfu t\u1ed1 tr\u00ean s\u1ebd quy\u1ebft \u0111\u1ecbnh h\u00ecnh d\u1ea1ng v\u00e0 k\u00edch th\u01b0\u1edbc c\u1ee7a h\u00ecnh n\u00f3n. Song, \u0111\u1ec3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c c\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n th\u00ec tr\u01b0\u1edbc h\u1ebft b\u1ea1n ph\u1ea3i hi\u1ec3u \u0111\u01b0\u1ee3c \u00fd ngh\u0129a c\u1ee7a t\u1eebng y\u1ebfu t\u1ed1 qua c\u00e1c th\u00f4ng s\u1ed1 sau:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u00e1n k\u00ednh \u0111\u00e1y (r): \u0110\u00e2y l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m c\u1ee7a \u0111\u00e1y \u0111\u1ebfn b\u1ea5t k\u1ef3 \u0111i\u1ec3m n\u00e0o tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n \u1edf \u0111\u00e1y.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Chi\u1ec1u cao (h): Chi\u1ec1u d\u00e0i t\u1eeb \u0111\u1ec9nh c\u1ee7a h\u00ecnh n\u00f3n \u0111\u1ebfn m\u1eb7t ph\u1eb3ng ch\u1ee9a \u0111\u01b0\u1eddng tr\u00f2n \u1edf \u0111\u00e1y.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u1ec9nh (V): \u0110\u00e2y l\u00e0 \u0111i\u1ec3m t\u1eadp trung c\u1ee7a h\u00ecnh n\u00f3n, n\u01a1i m\u00e0 t\u1ea5t c\u1ea3 c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1eeb \u0111\u1ec9nh \u0111\u1ebfn c\u00e1c \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n \u1edf \u0111\u00e1y c\u00f9ng nhau.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-298897 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u00ecn chung, c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n v\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n s\u1ebd th\u01b0\u1eddng \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng \u0111\u1ec3 m\u00f4 t\u1ea3 v\u00e0 t\u00ednh to\u00e1n trong nhi\u1ec1u l\u0129nh v\u1ef1c thu\u1ed9c l\u0129nh v\u1ef1c x\u00e2y d\u1ef1ng v\u00e0 thi\u1ebft k\u1ebf tr\u00ean th\u1ef1c t\u1ebf. Do \u0111\u00f3, n\u1ebfu mu\u1ed1n t\u00ecm hi\u1ec3u c\u00e1ch t\u00ednh v\u00e0 c\u00e1c b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn h\u00ecnh n\u00f3n th\u00ec qu\u00fd b\u1ea1n \u0111\u1ecdc n\u00ean tham kh\u1ea3o th\u00eam n\u1ed9i dung \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y d\u01b0\u1edbi \u0111\u00e2y.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">C\u00e1ch t\u00ednh ch\u00ednh x\u00e1c di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">C\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh n\u00f3n v\u00f4 c\u00f9ng \u0111\u01a1n gi\u1ea3n. B\u1ea1n c\u00f3 th\u1ec3 \u00e1p d\u00f9ng th\u00e0nh c\u00f4ng c\u00e1ch t\u00ednh n\u00e0y trong l\u1ea7n \u0111\u1ea7u ti\u00ean th\u1ef1c hi\u1ec7n th\u00f4ng qua g\u1ee3i \u00fd d\u01b0\u1edbi \u0111\u00e2y.<\/span><\/p>\n<h3><b>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n (To\u00e1n 9)<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n (kh\u00f4ng t\u00ednh \u0111\u00e1y) l\u00e0:<\/span><\/p>\n<p><b>Sxq = \u03c0 \u00d7 r \u00d7 l<\/b><\/p>\n<p><span style=\"font-weight: 400;\">(trong \u0111\u00f3: r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y, l l\u00e0 \u0111\u01b0\u1eddng sinh = \u221a(r\u00b2 + h\u00b2), \u03c0 \u2248 3,14).<\/span><\/p>\n<p><b>Ch\u1ee9ng minh ng\u1eafn g\u1ecdn:<\/b><span style=\"font-weight: 400;\"> M\u1eb7t xung quanh h\u00ecnh n\u00f3n khi tr\u1ea3i ph\u1eb3ng th\u00e0nh h\u00ecnh qu\u1ea1t tr\u00f2n c\u00f3 chu vi cung = chu vi \u0111\u00e1y (2\u03c0r), b\u00e1n k\u00ednh qu\u1ea1t = l \u2192 Sxq = (1\/2) \u00d7 2\u03c0r \u00d7 l = \u03c0rl.<\/span><\/p>\n<p><b>V\u00ed d\u1ee5 1 (SGK To\u00e1n 9):<\/b><span style=\"font-weight: 400;\"> H\u00ecnh n\u00f3n r = 5 cm, h = 8 cm. T\u00ednh Sxq.<\/span><\/p>\n<p><b>L\u1eddi gi\u1ea3i:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">l = \u221a(5\u00b2 + 8\u00b2) = \u221a(25 + 64) = \u221a89 cm.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sxq = \u03c0 \u00d7 5 \u00d7 \u221a89 \u2248 3,14 \u00d7 5 \u00d7 9,43 \u2248 148 cm\u00b2.<\/span><\/p>\n<p style=\"text-align: center;\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-298898 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-3.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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 style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Sxq l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a di\u1ec7n t\u00edch xung quanh.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">\u03c0 l\u00e0 h\u1eb1ng s\u1ed1 trong to\u00e1n h\u1ecdc, ch\u00fang \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 g\u1ea7n b\u1eb1ng 3,14.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">r l\u00e0 b\u00e1n k\u00ednh \u1edf ph\u1ea7n \u0111\u00e1y c\u1ee7a h\u00ecnh n\u00f3n.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">l l\u00e0 \u0111o\u1ea1n \u0111\u01b0\u1eddng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng sinh, n\u1ed1i \u0111\u1ec9nh c\u1ee7a n\u00f3n v\u1edbi \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n \u1edf \u0111\u00e1y. \u0110\u1ec3 t\u00ednh l, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Pythagoras v\u1edbi c\u00f4ng th\u1ee9c b\u1eb1ng c\u0103n b\u1eadc hai c\u1ee7a t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a r v\u00e0 h, v\u01a1i h la chi\u00eau cao c\u1ee7a h\u00ecnh n\u00f3n.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\"><strong>V\u00ed d\u1ee5 minh h\u1ecda<\/strong>: H\u00e3y xem x\u00e9t m\u1ed9t h\u00ecnh n\u00f3n c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r =5 v\u00e0 chi\u1ec1u cao \u210e = 8. B\u1ea1n h\u00e3y t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n trong \u0111\u1ec1 b\u00e0i tr\u00ean.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft<\/strong>:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Theo \u0111\u1ec1 b\u00e0i ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c l = <\/span><span style=\"font-weight: 400;\">(r)2 +( h)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">(5)2<\/span><span style=\"font-weight: 400;\">+(8)<\/span><span style=\"font-weight: 400;\">2<\/span> <span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">89<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady, di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh n\u00f3n trong b\u00e0i to\u00e1n n\u00e0y s\u1ebd b\u1eb1ng, Sxq = \u03c0 x r x l = \u03c0 x 5 x <\/span><span style=\"font-weight: 400;\">89<\/span><span style=\"font-weight: 400;\"> = 148<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">\u1ee8ng d\u1ee5ng c\u1ee7a vi\u1ec7c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Trong th\u1ef1c t\u1ebf, c\u00e1ch t\u00ednh di\u1ec7n t\u00edch c\u1ee7a xung quanh h\u00ecnh n\u00f3n \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong c\u00e1c l\u0129nh v\u1ef1c sau:<\/span><\/p>\n<p><b>Ch\u1ebf t\u1ea1o v\u00e0 x\u00e2y d\u1ef1ng<\/b><span style=\"font-weight: 400;\">: Trong vi\u1ec7c x\u00e2y d\u1ef1ng c\u00e1c c\u1ed9t, \u0111\u00e0i nh\u00e0 \u1edf ho\u1eb7c c\u00e1c c\u00f4ng tr\u00ecnh c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n, c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch xung quanh gi\u00fap x\u00e1c \u0111\u1ecbnh l\u01b0\u1ee3ng v\u1eadt li\u1ec7u c\u1ea7n thi\u1ebft \u0111\u1ec3 b\u1ecdc v\u00e0 ho\u00e0n thi\u1ec7n b\u1ec1 m\u1eb7t ngo\u1ea1i c\u1ee7a c\u1ea5u tr\u00fac. Th\u1eadm ch\u00ed, \u00e1p d\u1ee5ng c\u00f4ng th\u1ef1c t\u00ednh n\u00e0y c\u00f2n b\u1ea1n t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c nh\u1eefng nguy\u00ean v\u1eadt li\u1ec7u c\u1ea7n thi\u1ebft \u0111\u1ec3 thi c\u00f4ng v\u00e0 thi\u1ebft k\u1ebf d\u1ef1 \u00e1n.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298899 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-4.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><b>Ng\u00e0nh c\u00f4ng nghi\u1ec7p<\/b><span style=\"font-weight: 400;\">: Trong thi\u1ebft k\u1ebf bao b\u00ec c\u00f3 h\u00ecnh d\u1ea1ng h\u00ecnh n\u00f3n, vi\u1ec7c \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n di\u1ec7n t\u00edch xung quanh gi\u00fap nh\u00e0 s\u1ea3n xu\u1ea5t \u01b0\u1edbc l\u01b0\u1ee3ng \u0111\u01b0\u1ee3c c\u00e1c v\u1eadt li\u1ec7u c\u1ea7n s\u1eed d\u1ee5ng \u0111\u1ec3 s\u1ea3n xu\u1ea5t bao b\u00ec theo y\u00eau c\u1ea7u. Th\u1eadm ch\u00ed, ch\u00fang c\u00f2n gi\u00fap b\u1ea1n t\u00ednh to\u00e1n ch\u00ednh x\u00e1c kh\u00f4ng gian ch\u1ee9a \u0111\u1ef1ng s\u1ea3n ph\u1ea9m trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y.<\/span><\/p>\n<p><b>Trong gi\u00e1o d\u1ee5c:<\/b><span style=\"font-weight: 400;\"> C\u00f4ng th\u1ee9c di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n th\u01b0\u1eddng xu\u1ea5t hi\u1ec7n trong c\u00e1c b\u00e0i to\u00e1n to\u00e1n h\u1ecdc v\u00e0 tr\u00ean c\u00e1c \u0111\u1ec1 thi. \u0110i\u1ec1u n\u00e0y gi\u00fap h\u1ecdc sinh v\u00e0 sinh vi\u00ean n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u1ec1 to\u00e1n h\u1ecdc \u0111\u1ec3 \u00e1p d\u1ee5ng trong th\u1ef1c t\u1ebf.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">C\u00e1ch t\u00ednh ch\u00ednh x\u00e1c di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh n\u00f3n<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Th\u1ef1c t\u1ebf, c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n \u0111\u01b0\u1ee3c c\u1ea5u th\u00e0nh d\u1ef1a tr\u00ean n\u1ec1n t\u1ea3ng c\u1ee7a c\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh. B\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam n\u1ed9i dung \u0111\u01b0\u1ee3c ch\u00fang t\u00f4i g\u1ee3i \u00fd d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c t\u00ednh v\u00e0 c\u00e1ch t\u00ednh c\u1ee7a lo\u1ea1i h\u00ecnh \u0111\u1eb7c bi\u1ec7t n\u00e0y.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n bao g\u1ed3m c\u1ea3 di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n v\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y. \u0110\u1ec3 t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n (Stp), ch\u00fang ta s\u1ebd s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c nh\u01b0 sau:<\/span><\/p>\n<p style=\"text-align: center;\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298900 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-5.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Stp l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Sxq l\u00e0 di\u1ec7n t\u00edch xung quanh. C\u00f4ng th\u1ee9c n\u00e0y \u0111\u00e3 \u0111\u01b0\u1ee3c h\u01b0\u1edbng d\u1eabn c\u1ee5 th\u1ec3 b\u00ean tr\u00ean.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u03c0 l\u00e0 h\u1eb1ng s\u1ed1 trong to\u00e1n h\u1ecdc, ch\u00fang \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 g\u1ea7n b\u1eb1ng 3,14.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">r l\u00e0 b\u00e1n k\u00ednh \u1edf ph\u1ea7n \u0111\u00e1y c\u1ee7a h\u00ecnh n\u00f3n.<\/span><\/li>\n<\/ul>\n<p><b>L\u01b0u \u00fd<\/b><span style=\"font-weight: 400;\">: Di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh n\u00f3n ch\u1ec9 l\u00e0 c\u00f4ng th\u1ee9c t\u00ednh ph\u1ea7n b\u00ean ngo\u00e0i h\u00ecnh n\u00f3n, trong khi di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n bao g\u1ed3m c\u1ea3 ph\u1ea7n xung quanh v\u00e0 ph\u1ea7n \u0111\u00e1y. Do \u0111\u00f3, b\u1ea1n c\u1ea7n ch\u00fa \u00fd s\u1eed d\u1ee5ng ch\u00ednh x\u00e1c c\u00f4ng th\u1ee9c c\u1ee7a hai c\u00e1ch t\u00ednh n\u00e0y \u0111\u1ec3 cho ra k\u1ebft qu\u1ea3 chu\u1ea9n nh\u1ea5t.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>V\u00ed d\u1ee5 minh h\u1ecda<\/strong>: Gi\u1ea3 s\u1eed ch\u00fang ta c\u00f3 m\u1ed9t h\u00ecnh n\u00f3n c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r = 6 v\u00e0 chi\u1ec1u cao h = 10. H\u00e3y t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n b\u00ean tr\u00ean.<\/span><\/p>\n<p><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">D\u1ef1a v\u00e0o s\u1ed1 li\u1ec7u \u0111\u00e3 cho, ta c\u00f3 l =\u00a0 l = <\/span><span style=\"font-weight: 400;\">(r)2 +( h)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">(6)2<\/span><span style=\"font-weight: 400;\">+(10)<\/span><span style=\"font-weight: 400;\">2<\/span> <span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">136<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3, ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n nh\u01b0 sau: Sxq = \u03c0 x r x l = \u03c0 x 6 x <\/span><span style=\"font-weight: 400;\">136<\/span><span style=\"font-weight: 400;\"> = 220<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n tr\u00ean s\u1ebd c\u00f3 k\u1ebft qu\u1ea3 l\u00e0 Stp = Sxq + \u03c0 x (r)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">= 333<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">\u1ee8ng d\u1ee5ng c\u1ee7a vi\u1ec7c t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh n\u00f3n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Vi\u1ec7c t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong nhi\u1ec1u l\u0129nh v\u1ef1c \u0111\u1eddi s\u1ed1ng. C\u1ee5 th\u1ec3, trong ki\u1ebfn tr\u00fac v\u00e0 x\u00e2y d\u1ef1ng, vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a c\u1ed9t c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n gi\u00fap x\u00e1c \u0111\u1ecbnh l\u01b0\u1ee3ng v\u1eadt li\u1ec7u c\u1ea7n thi\u1ebft \u0111\u1ec3 ho\u00e0n thi\u1ec7n c\u1ea3 ph\u1ea7n b\u1ec1 m\u1eb7t xung quanh v\u00e0 \u0111\u1ec9nh. Nh\u01b0 v\u1eady, khi thi\u1ebft k\u1ebf c\u00e1c \u0111\u00e0i phun n\u01b0\u1edbc c\u00f3 h\u00ecnh d\u1ea1ng h\u00ecnh n\u00f3n, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n s\u1ebd quy\u1ebft \u0111\u1ecbnh l\u01b0\u1ee3ng v\u1eadt li\u1ec7u s\u01a1n ho\u1eb7c v\u1eadt li\u1ec7u trang tr\u00ed c\u1ea7n s\u1eed d\u1ee5ng.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298901 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-6.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong l\u0129nh v\u1ef1c c\u00f4ng nghi\u1ec7p, t\u00ednh to\u00e1n di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n l\u00e0 quan tr\u1ecdng trong ch\u1ebf t\u1ea1o b\u00ecnh ch\u1ee9a h\u00ecnh n\u00f3n. Vi\u1ec7c x\u00e1c \u0111\u1ecbnh di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t c\u1ea7n \u0111\u01b0\u1ee3c x\u1eed l\u00fd ho\u1eb7c ph\u1ee7 gi\u00fap \u0111\u1ea3m b\u1ea3o ch\u1ea5t l\u01b0\u1ee3ng v\u00e0 an to\u00e0n c\u1ee7a b\u00ecnh ch\u1ee9a. \u0110\u1eb7c bi\u1ec7t l\u00e0 khi n\u00f3 li\u00ean quan \u0111\u1ebfn c\u00e1c nguy\u00ean li\u1ec7u nh\u01b0 h\u00f3a ch\u1ea5t ho\u1eb7c d\u1ea7u. Th\u1eadm ch\u00ed trong ng\u00e0nh in 3D, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a m\u1ed9t h\u00ecnh n\u00f3n \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn l\u01b0\u1ee3ng v\u1eadt li\u1ec7u c\u1ea7n s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ea1o ra s\u1ea3n ph\u1ea9m. T\u1eeb \u0111\u00f3 gi\u00fap cho c\u00f4ng th\u1ee9c n\u00e0y tr\u1edf n\u00ean quan tr\u1ecdng trong qu\u00e1 tr\u00ecnh s\u1ea3n xu\u1ea5t.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298902 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-7.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i ra, c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n c\u00f2n c\u00f3 \u1ee9ng d\u1ee5ng trong gi\u00e1o d\u1ee5c v\u00e0 nghi\u00ean c\u1ee9u trong \u0111\u1eddi s\u1ed1ng. C\u00f4ng th\u1ee9c n\u00e0y v\u00e0 c\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n c\u0169ng th\u01b0\u1eddng xu\u1ea5t hi\u1ec7n trong c\u00e1c b\u00e0i to\u00e1n. \u0110i\u1ec1u n\u00e0y gi\u00fap h\u1ecdc sinh n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u00e0 k\u1ef9 n\u0103ng to\u00e1n h\u1ecdc c\u01a1 b\u1ea3n khi c\u00f2n ng\u1ed3i tr\u00ean gh\u1ebf nh\u00e0 tr\u01b0\u1eddng.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">C\u00e1ch t\u00ednh ch\u00ednh x\u00e1c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n \u0111\u01a1n gi\u1ea3n d\u00e0nh cho b\u1ea1n<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Kh\u00e1c v\u1edbi c\u00f4ng th\u1ee9c c\u1ee7a di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n, c\u00e1ch t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh h\u1ecdc kh\u00f4ng gian n\u00e0y nh\u00ecn chung s\u1ebd c\u00f3 ph\u1ea7n \u0111\u1eb7c bi\u1ec7t h\u01a1n. C\u1ee5 th\u1ec3 nh\u01b0 sau:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh n\u00f3n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n l\u00e0 kh\u00f4ng gian m\u00e0 h\u00ecnh h\u1ecdc n\u00e0y chi\u1ebfm \u0111\u1ef1ng. Do \u0111\u00f3, \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n th\u00ec ng\u01b0\u1eddi d\u00f9ng ph\u1ea3i \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1eb7c bi\u1ec7t nh\u01b0 sau:<\/span><\/p>\n<p style=\"text-align: center;\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298903 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-8.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">V l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n<\/span><\/li>\n<li><span style=\"font-weight: 400;\">\u03c0 l\u00e0 h\u1eb1ng s\u1ed1 trong to\u00e1n h\u1ecdc, ch\u00fang \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 g\u1ea7n b\u1eb1ng 3,14.<\/span><\/li>\n<li><span style=\"font-weight: 400;\">r v\u00e0 h l\u1ea7n l\u01b0\u1ee3t l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y v\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh n\u00f3n.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\"><strong>V\u00ed d\u1ee5 minh h\u1ecda<\/strong>: Gi\u1ea3 s\u1eed \u0111\u1ec1 b\u00e0i cho m\u1ed9t h\u00ecnh n\u00f3n c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r = 4 v\u00e0 chi\u1ec1u cao h = 9. B\u1ea1n h\u00e3y, t\u00ednh th\u1ec3 t\u00edch v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n tr\u00ean.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft<\/strong>:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Theo \u0111\u1ec1 b\u00e0i ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c l = <\/span><span style=\"font-weight: 400;\">(r)2 +( h)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = <\/span><span style=\"font-weight: 400;\">(4)2<\/span><span style=\"font-weight: 400;\">+(9)<\/span><span style=\"font-weight: 400;\">2<\/span> <span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">97<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch xung quanh h\u00ecnh tr\u1ee5 l\u00e0 Sxq = \u03c0 x r x l = \u03c0 x 4 x <\/span><span style=\"font-weight: 400;\">97<\/span><span style=\"font-weight: 400;\"> = 124<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3, ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh n\u00f3n nh\u01b0 sau: Stp = Sxq + \u03c0 x (r)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">= 174<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady, th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh t\u1ee5 c\u1ea7n t\u00ecm l\u00e0\u00a0 V = <\/span><span style=\"font-weight: 400;\">1<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">\u03c0 x r<\/span><span style=\"font-weight: 400;\">2 <\/span><span style=\"font-weight: 400;\">x h = 48\u03c0<\/span><\/li>\n<\/ul>\n<h3><span style=\"font-weight: 400;\">\u1ee8ng d\u1ee5ng c\u1ee7a vi\u1ec7c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Vi\u1ec7c t\u00ednh to\u00e1n th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n kh\u00f4ng ch\u1ec9 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng m\u00e0 c\u00f2n c\u00f3 nh\u1eefng \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i v\u00e0 th\u1ef1c t\u1ebf trong nhi\u1ec1u l\u0129nh v\u1ef1c cu\u1ed9c s\u1ed1ng. C\u1ee5 th\u1ec3, trong qu\u1ea3n l\u00fd dung l\u01b0\u1ee3ng v\u00e0 l\u01b0u tr\u1eef, vi\u1ec7c t\u00ednh to\u00e1n th\u1ec3 t\u00edch gi\u00fap d\u1ef1 \u0111o\u00e1n v\u00e0 qu\u1ea3n l\u00fd kho ch\u1ee9a, t\u1eeb c\u00e1c th\u00f9ng ch\u1ee9a h\u00e0ng h\u00f3a \u0111\u1ebfn c\u00e1c b\u1ec3 ch\u1ee9a n\u01b0\u1edbc l\u1edbn. \u0110i\u1ec1u n\u00e0y gi\u00fap ng\u01b0\u1eddi d\u00f9ng ti\u1ebft ki\u1ec7m c\u00f4ng s\u1ee9c v\u00e0 t\u1ed1i \u01b0u h\u00f3a \u0111\u01b0\u1ee3c th\u1eddi gian trong qu\u00e1 tr\u00ecnh th\u1ef1c hi\u1ec7n nhi\u1ec7m v\u1ee5.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-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-298904 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-9.jpg\" alt=\"dien-tich-xung-quanh-hinh-non-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/dien-tich-xung-quanh-hinh-non-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Trong ng\u00e0nh s\u1ea3n xu\u1ea5t v\u00e0 \u0111\u00f3ng g\u00f3i, th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n \u0111\u01b0\u1ee3c xem l\u00e0 c\u00f4ng th\u1ee9c quan tr\u1ecdng trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh l\u01b0\u1ee3ng v\u1eadt li\u1ec7u c\u1ea7n s\u1eed d\u1ee5ng cho thi\u1ebft k\u1ebf bao b\u00ec, chai l\u1ecd hay th\u1eadm ch\u00ed c\u1ea3 \u0111\u00f3ng g\u00f3i s\u1ea3n ph\u1ea9m trong c\u00e1c th\u00f9ng ch\u1ee9a c\u00f3 d\u1ea1ng h\u00ecnh n\u00f3n. \u0110i\u1ec1u n\u00e0y gi\u00fap t\u1ed1i \u01b0u h\u00f3a kh\u00f4ng gian ch\u1ee9a s\u1ea3n ph\u1ea9m v\u00e0 ngu\u1ed3n l\u1ef1c gia c\u00f4ng. Th\u1eadm ch\u00ed, c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh n\u00f3n c\u0169ng th\u01b0\u1eddng xu\u1ea5t hi\u1ec7n trong c\u00e1c b\u00e0i to\u00e1n v\u00e0 \u0111\u1ec1 thi. \u0110i\u1ec1u n\u00e0y gi\u00fap h\u1ecdc sinh v\u00e0 sinh vi\u00ean c\u00f3 \u0111\u01b0\u1ee3c s\u1ef1 hi\u1ec3u bi\u1ebft s\u00e2u s\u1eafc v\u1ec1 c\u00e1ch \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c \u0111\u00e3 h\u1ecdc c\u1ee7a m\u00ecnh v\u00e0o th\u1ef1c t\u1ebf.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">L\u1eddi k\u1ebft<\/span><\/h2>\n<p><i><span style=\"font-weight: 400;\">Nh\u00ecn chung, c\u00e1ch t\u00ednh th\u1ec3 t\u00edch, di\u1ec7n t\u00edch to\u00e0n th\u00e0nh v\u00e0 <\/span><\/i><b><i>di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n<\/i><\/b><i><span style=\"font-weight: 400;\"> kh\u00e1 \u0111\u01a1n gi\u1ea3n. Th\u1eadm ch\u00ed, c\u00f4ng th\u1ee9c \u0111\u1ec3 th\u1ef1c hi\u1ec7n thao t\u00e1c t\u00ednh to\u00e1n c\u0169ng d\u1ec5 nh\u1edb v\u00e0 d\u1ec5 hi\u1ec3u. N\u1ebfu kh\u00f4ng nh\u1edb c\u00f4ng th\u1ee9c, ch\u1ec9 c\u1ea7n b\u1ea1n xem l\u1ea1i nh\u1eefng g\u1ee3i \u00fd \u0111\u01b0\u1ee3c <\/span><\/i><b><i>Ho\u00e0ng H\u00e0 Mobile<\/i><\/b><i><span style=\"font-weight: 400;\"> tr\u00ecnh b\u00e0y b\u00ean tr\u00ean. Th\u1eadm ch\u00ed, h\u00e3y \u0111\u1ec3 l\u1ea1i b\u00ecnh lu\u1eadn b\u00ean d\u01b0\u1edbi n\u1ebfu g\u1eb7p c\u00e1c v\u1ea5n \u0111\u1ec1 trong qu\u00e1 tr\u00ecnh theo d\u00f5i b\u00e0i vi\u1ebft \u0111\u1ec3 nh\u1eadn \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p c\u1ee5 th\u1ec3 h\u01a1n nh\u00e9!<\/span><\/i><\/p>\n<p><i><span style=\"font-weight: 400;\">XEM TH\u00caM<\/span><\/i><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-tinh-dien-tich-hinh-thang\/\">C\u00e1ch t\u00ednh di\u1ec7n t\u00edch h\u00ecnh thang &amp; h\u00ecnh thang vu\u00f4ng, b\u00e0i t\u1eadp th\u1ef1c h\u00e0nh minh h\u1ecda chi ti\u1ebft<\/a><\/strong><\/li>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-thuc-la-gi\/\">S\u1ed1 th\u1ef1c l\u00e0 g\u00ec? M\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n h\u1ecdc ph\u1ed5 bi\u1ebfn v\u1ec1 s\u1ed1 th\u1ef1c<\/a><\/strong><\/li>\n<li style=\"font-weight: 400;\"><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-vuong\/\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng ch\u00ednh x\u00e1c nh\u1ea5t<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n (Sxq = \u03c0.r.l) l\u00e0 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n To\u00e1n 9, \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh t\u1eeb vi\u1ec7c quay tam gi\u00e1c vu\u00f4ng quanh c\u1ea1nh g\u00f3c vu\u00f4ng. B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn chi ti\u1ebft c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n (Stp = \u03c0.r.l + \u03c0.r\u00b2), th\u1ec3 t\u00edch [&hellip;]<\/p>\n","protected":false},"author":101,"featured_media":298895,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-298894","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 di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n chi ti\u1ebft | Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n &amp; th\u1ec3 t\u00edch<\/title>\n<meta name=\"description\" content=\"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n: Sxq = \u03c0.r.l. 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