{"id":299661,"date":"2023-12-25T20:14:34","date_gmt":"2023-12-25T13:14:34","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=299661"},"modified":"2023-12-25T20:14:34","modified_gmt":"2023-12-25T13:14:34","slug":"the-tich-khoi-cau","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-cau\/","title":{"rendered":"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u l\u00e0 ki\u1ebfn th\u1ee9c m\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea7n ph\u1ea3i n\u1eafm v\u1eefng \u0111\u1ec3 chu\u1ea9n b\u1ecb cho nh\u1eefng k\u1ef3 thi s\u1eafp \u0111\u1ebfn. Vi\u1ec7c n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c n\u00e0y c\u0169ng gi\u00fap b\u1ea1n \u00f4n thi v\u00e0 l\u00e0m b\u00e0i t\u1eadp nhanh ch\u00f3ng h\u01a1n. N\u1ebfu c\u00e1c b\u1ea1n v\u1eabn ch\u01b0a hi\u1ec3u r\u00f5 v\u1ec1 h\u00ecnh c\u1ea7u v\u00e0 nh\u1eefng c\u00f4ng th\u1ee9c xung quanh n\u00f3 th\u00ec c\u00f3 th\u1ec3 t\u00ecm hi\u1ec3u qua b\u00e0i vi\u1ebft sau \u0111\u00e2y.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">H\u00ecnh c\u1ea7u, m\u1eb7t c\u1ea7u l\u00e0 g\u00ec?<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Tr\u01b0\u1edbc khi t\u00ecm hi\u1ec3u th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u, di\u1ec7n t\u00edch kh\u1ed1i c\u1ea7u th\u00ec ch\u00fang ta ph\u1ea3i t\u00ecm hi\u1ec3u v\u1ec1 h\u00ecnh c\u1ea7u, m\u1eb7t c\u1ea7u. Trong kh\u00f4ng gian 3 chi\u1ec1u theo to\u00e1n h\u1ecdc th\u00ec khi ch\u00fang ta quay 1 n\u1eeda h\u00ecnh tr\u00f2n (v\u1edbi t\u00e2m l\u00e0 O v\u00e0 R l\u00e0 b\u00e1n k\u00ednh) quanh 1 \u0111\u01b0\u1eddng k\u00ednh c\u1ed1 \u0111\u1ecbnh c\u00f3 t\u00ean l\u00e0 AB th\u00ec ch\u00fang ta s\u1ebd nh\u1eadn \u0111\u01b0\u1ee3c m\u1ed9t h\u00ecnh c\u1ea7u:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">N\u1eeda h\u00ecnh tr\u00f2n c\u1ee7a ph\u00e9p quay \u1edf tr\u00ean ch\u00ednh l\u00e0 m\u1ed9t m\u1eb7t c\u1ea7u.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">O \u0111\u01b0\u1ee3c coi l\u00e0 t\u00e2m c\u1ee7a h\u00ecnh c\u1ea7u v\u00e0 R ch\u00ednh l\u00e0 b\u00e1n k\u00ednh trong m\u1eb7t c\u1ea7u hay h\u00ecnh c\u1ea7u \u0111\u00f3.<\/span><\/li>\n<\/ul>\n<figure id=\"attachment_299664\" aria-describedby=\"caption-attachment-299664\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-299664 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-1.jpg\" alt=\"the-tich-khoi-cau-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299664\" class=\"wp-caption-text\">H\u00ecnh c\u1ea7u l\u00e0 g\u00ec?<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">M\u1eb7t c\u1ea7u g\u1ed3m nh\u1eefng \u0111i\u1ec3m n\u1eb1m c\u00e1ch t\u00e2m O c\u1ee7a h\u00ecnh c\u1ea7u m\u1ed9t kho\u1ea3ng c\u00e1ch c\u1ed1 \u0111\u1ecbnh \u0111\u00e3 cho s\u1eb5n v\u00e0 kh\u00f4ng \u0111\u1ed5i. \u0110\u00e2y ch\u00ednh l\u00e0 b\u00e1n k\u00ednh R v\u00e0 R = OA.<\/span><\/p>\n<figure id=\"attachment_299665\" aria-describedby=\"caption-attachment-299665\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"wp-image-299665 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-2.jpg\" alt=\"the-tich-khoi-cau-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299665\" class=\"wp-caption-text\">M\u1eb7t c\u1ea7u l\u00e0 g\u00ec?<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i ra h\u00ecnh c\u1ea7u c\u00f2n m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t nh\u01b0 sau:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">B\u1ea5t c\u1ee9 \u0111\u01b0\u1eddng th\u1eb3ng giao v\u1edbi h\u00ecnh c\u1ea7u r\u1ed3i \u0111i ngang qua t\u00e2m h\u00ecnh c\u1ea7u \u0111\u1ec1u l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng trong h\u00ecnh c\u1ea7u. L\u00fac \u0111\u00f3 khi quay m\u1ed9t qu\u1ea3 c\u1ea7u \u0111i quanh tr\u1ee5c \u0111\u1ed1i x\u1ee9ng d\u00f9 \u1edf g\u00f3c n\u00e0o c\u0169ng khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh ch\u00ednh n\u00f3.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u1eb7t ph\u1eb3ng ph\u1ea3n x\u1ea1 trong h\u00ecnh c\u1ea7u l\u00e0 m\u1eb7t ph\u1eb3ng c\u00f3 th\u1ec3 c\u1eaft h\u00ecnh c\u1ea7u \u0111i ngang qua t\u00e2m h\u00ecnh c\u1ea7u v\u00e0 chia h\u00ecnh n\u00e0y ra 2 ph\u1ea7n nh\u01b0 nhau.<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u v\u00e0 di\u1ec7n t\u00edch kh\u1ed1i c\u1ea7u<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau khi \u0111\u00e3 t\u00ecm hi\u1ec3u s\u01a1 l\u01b0\u1ee3c v\u1ec1 h\u00ecnh c\u1ea7u v\u00e0 m\u1eb7t c\u1ea7u th\u00ec ti\u1ebfp theo c\u00e1c b\u1ea1n h\u00e3y t\u00ecm hi\u1ec3u c\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u nh\u01b0 sau:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch (S) c\u1ee7a m\u1eb7t c\u1ea7u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Theo kh\u00e1i ni\u1ec7m \u1edf tr\u00ean th\u00ec S m\u1eb7t c\u1ea7u g\u1ea5p 4 l\u1ea7n S c\u1ee7a h\u00ecnh tr\u00f2n to ho\u1eb7c g\u1ea5p 4 l\u1ea7n Pi (\u03c0) \u0111em nh\u00e2n v\u1edbi b\u00e1n k\u00ednh b\u00ecnh ph\u01b0\u01a1ng thu\u1ed9c h\u00ecnh c\u1ea7u.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady c\u00e1ch t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u l\u00e0: S = 4\u03c0 x r^2 = \u03c0 x d^2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S: Di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">r: B\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u\/ m\u1eb7t c\u1ea7u<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">d: \u0110\u01b0\u1eddng k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u\/ m\u1eb7t c\u1ea7u<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u03c0: h\u1eb1ng s\u1ed1 x\u1ea5p x\u1ec9 3,14<\/span><\/li>\n<\/ul>\n<figure id=\"attachment_299666\" aria-describedby=\"caption-attachment-299666\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"wp-image-299666 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-3.jpg\" alt=\"the-tich-khoi-cau-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299666\" class=\"wp-caption-text\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch (S) c\u1ee7a m\u1eb7t c\u1ea7u<\/figcaption><\/figure>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch (S) h\u00ecnh c\u1ea7u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c S h\u00ecnh c\u1ea7u th\u00ec c\u00e1c b\u1ea1n d\u00f9ng c\u00f4ng th\u1ee9c: Sxq\u00a0 = 4 x \u03c0 x r^2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Sxq: Di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u03c0: H\u1eb1ng s\u1ed1 3,14<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">r: b\u00e1n k\u00ednh h\u00ecnh c\u1ea7u<\/span><\/li>\n<\/ul>\n<figure id=\"attachment_299667\" aria-describedby=\"caption-attachment-299667\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-299667 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-4.jpg\" alt=\"the-tich-khoi-cau-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299667\" class=\"wp-caption-text\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch (S) h\u00ecnh c\u1ea7u<\/figcaption><\/figure>\n<h3><span style=\"font-weight: 400;\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n th\u1ec3 t\u00edch (V) c\u1ee7a h\u00ecnh c\u1ea7u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u th\u00ec b\u1ea1n c\u1ea7n t\u00ecm ra b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u ho\u1eb7c t\u00ecm \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u. Ti\u1ebfp \u0111\u00f3 th\u00ec b\u1ea1n thay th\u1ebf ch\u00fang cho c\u00f4ng th\u1ee9c sau:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V = (4 x \u03c0 x r^3)\/ 3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">V: Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u (m3)<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u03c0: Gi\u00e1 tr\u1ecb g\u1ea7n b\u1eb1ng 3,14<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">r: B\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">d: B\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u\/ m\u1eb7t c\u1ea7u<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Ch\u00fa \u00fd: Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u c\u00f3 \u0111\u01a1n v\u1ecb l\u00e0 kh\u1ed1i (m3, cm3,&#8230;)<\/span><\/p>\n<figure id=\"attachment_299668\" aria-describedby=\"caption-attachment-299668\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-299668 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-5.jpg\" alt=\"the-tich-khoi-cau-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299668\" class=\"wp-caption-text\">C\u00f4ng th\u1ee9c d\u00f9ng \u0111\u1ec3 t\u00ednh to\u00e1n th\u1ec3 t\u00edch (V) c\u1ee7a h\u00ecnh c\u1ea7u<\/figcaption><\/figure>\n<h2><span style=\"font-weight: 400;\">H\u01b0\u1edbng d\u1eabn chi ti\u1ebft ph\u01b0\u01a1ng ph\u00e1p t\u00ednh to\u00e1n th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau \u0111\u00e2y l\u00e0 t\u1eebng b\u01b0\u1edbc t\u00ednh to\u00e1n th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u m\u00e0 c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp:<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u01b0\u1edbc 1: Vi\u1ebft v\u00e0o gi\u1ea5y c\u00f4ng th\u1ee9c t\u00ednh V h\u00ecnh c\u1ea7u<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">L\u00fac n\u00e0y b\u1ea1n c\u1ea7n vi\u1ebft c\u00f4ng th\u1ee9c V = (4 x \u03c0 x r^3)\/ 3 ra gi\u1ea5y \u0111\u1ec3 ti\u1ec7n cho vi\u1ec7c t\u00ednh to\u00e1n t\u1eebng th\u00e0nh ph\u1ea7n trong c\u00f4ng th\u1ee9c m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c.<\/span><\/p>\n<figure id=\"attachment_299669\" aria-describedby=\"caption-attachment-299669\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-299669 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-6.jpg\" alt=\"the-tich-khoi-cau-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299669\" class=\"wp-caption-text\">H\u01b0\u1edbng d\u1eabn chi ti\u1ebft ph\u01b0\u01a1ng ph\u00e1p t\u00ednh to\u00e1n th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u<\/figcaption><\/figure>\n<h3><span style=\"font-weight: 400;\">B\u01b0\u1edbc 2: \u0110\u1ecdc k\u0129 \u0111\u1ec1 b\u00e0i, t\u00ecm b\u00e1n k\u00ednh<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Ti\u1ebfp \u0111\u00f3 th\u00ec b\u1ea1n h\u00e3y \u0111\u1ecdc k\u1ef9 th\u00f4ng tin cho trong \u0111\u1ec1 b\u00e0i. N\u1ebfu \u0111\u1ec1 b\u00e0i \u0111\u00e3 c\u00f3 s\u1eb5n \u0111\u1ed9 d\u00e0i b\u00e1n k\u00ednh th\u00ec b\u1ea1n ti\u1ebfp t\u1ee5c ghi n\u00f3 ra gi\u1ea5y. Nh\u01b0ng \u0111\u1ec1 b\u00e0i m\u00e0 cho s\u1eb5n \u0111\u01b0\u1eddng k\u00ednh th\u00ec m\u1ecdi ng\u01b0\u1eddi c\u00f3 th\u1ec3 d\u00f9ng c\u00f4ng th\u1ee9c l\u00e0 V = 1\/6 x \u03c0 x d^3. Ho\u1eb7c c\u00e1c b\u1ea1n l\u1ea5y \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u \u0111em chia cho 2 \u0111\u1ec3 t\u00ecm b\u00e1n k\u00ednh v\u00e0 d\u00f9ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u \u0111\u00e3 ghi ra \u1edf b\u01b0\u1edbc 1.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">N\u1ebfu b\u00e0i to\u00e1n kh\u00f3 h\u01a1n v\u00e0 ch\u1ec9 cho s\u1eb5n d\u1eef li\u1ec7u v\u1ec1 S c\u1ee7a m\u1eb7t c\u1ea7u, c\u00e1c b\u1ea1n s\u1ebd t\u00ecm \u0111\u01b0\u1ee3c b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u b\u1eb1ng vi\u1ec7c l\u1ea5y S m\u1eb7t c\u1ea7u \u0111em chia 4\u03c0. Sau \u0111\u00f3 th\u00ec b\u1ea1n l\u1ea5y k\u1ebft qu\u1ea3 n\u00e0y b\u1ecf v\u00e0o c\u0103n b\u1eadc 2 \u0111\u1ec3 t\u00ednh. C\u1ee5 th\u1ec3 c\u00f4ng th\u1ee9c t\u00ednh b\u00e1n k\u00ednh h\u00ecnh c\u1ea7u theo c\u00e1ch n\u00e0y l\u00e0: r = \u221a(S\/4\u03c0).<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u01b0\u1edbc 3: T\u00edch to\u00e1n l\u0169y th\u1eeba \u1edf b\u1eadc ba c\u1ee7a r<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Ti\u1ebfp theo b\u1ea1n h\u00e3y t\u00ednh to\u00e1n l\u0169y th\u1eeba \u1edf b\u1eadc ba c\u1ee7a r b\u1eb1ng vi\u1ec7c l\u1ea5y b\u00e1n k\u00ednh \u0111i nh\u00e2n 3 l\u1ea7n cho ch\u00ednh n\u00f3 ho\u1eb7c b\u1ea1n c\u00f3 th\u1ec3 n\u00e2ng b\u00e1n k\u00ednh l\u00ean m\u1ed9t s\u1ed1 c\u00f3 m\u0169 3.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ch\u1eb3ng h\u1ea1n: (2cm)^3 = 2cm x 2cm x 2cm = 8<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(3cm)^3 = 3cm x 3cm x 3cm = 27<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u01b0\u1edbc 4: Nh\u00e2n s\u1ed1 l\u0169y th\u1eeba \u1edf b\u1eadc ba c\u1ee7a r cho 4\/3<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Sau \u0111\u00f3, c\u00e1c b\u1ea1n thay th\u1ebf k\u1ebft qu\u1ea3 r^3 \u0111\u00e3 t\u00ednh v\u00e0o V = (4 x \u03c0 x r^3)\/ 3 cho c\u00f4ng th\u1ee9c\u00a0 g\u1ecdn h\u01a1n. Ch\u1eb3ng h\u1ea1n b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u l\u00e0 1 cm th\u00ec ta c\u00f3 th\u1ec3 t\u00edch l\u00e0 V = 4\/3 x \u03c0 x 1 ho\u1eb7c V = 4\/3\u03c0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u01b0\u1edbc 5: B\u1ea1n nh\u00e2n k\u1ebft qu\u1ea3 \u1edf tr\u00ean v\u1edbi s\u1ed1 Pi c\u1ee5 th\u1ec3<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Sau c\u00f9ng, b\u1ea1n h\u00e3y \u0111\u1eb7t s\u1ed1 Pi c\u1ee5 th\u1ec3 v\u00e0o c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u v\u00e0 nh\u00e2n 3,14 v\u1edbi 4\/3. Ho\u1eb7c b\u1ea1n c\u00f3 th\u1ec3 \u0111\u1eb7t lu\u00f4n s\u1ed1 \u03c0 trong k\u1ebft qu\u1ea3 theo ki\u1ec3u V = 4\/3\u03c0 l\u00e0 ho\u00e0n t\u1ea5t.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ch\u1eb3ng h\u1ea1n V = 4\/3 x 3,14 = 4,19 cm3. V\u1eady th\u00ec k\u1ebft lu\u1eadn th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u c\u00f3 b\u00e1n k\u00ednh l\u00e0 1.<\/span><\/p>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n v\u1ec1 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u, di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u k\u00e8m l\u1eddi gi\u1ea3i<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Ngo\u00e0i vi\u1ec7c t\u00ecm hi\u1ec3u c\u00f4ng th\u1ee9c t\u00ednh V h\u00ecnh c\u1ea7u th\u00ec c\u00e1c b\u1ea1n n\u00ean t\u00ecm hi\u1ec3u th\u00eam m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp \u0111\u1ec3 \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c n\u00e0y.<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 1<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: Cho m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m l\u00e0 O, \u0111\u1ed9 d\u00e0i b\u00e1n k\u00ednh = 9m. B\u1ea1n h\u00e3y t\u00ednh S c\u1ee7a h\u00ecnh c\u1ea7u?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n: \u0110\u1ea7u ti\u00ean, b\u1ea1n l\u1ea5y \u0111\u1ed9 d\u00e0i c\u1ee7a b\u00e1n k\u00ednh thay cho c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u l\u00e0 4 x \u03c0 x R^2 v\u00e0 \u0111\u01b0\u1ee3c:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch = 4 x 3,14 x 9^2 = 1017,36 (m2)<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 2<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: Cho 1 \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m l\u00e0 O v\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng k\u00ednh = 2,5cm. B\u1ea1n h\u00e3y t\u00ednh S c\u1ee7a m\u1eb7t c\u1ea7u n\u00e0y?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n: \u0110\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c S c\u1ee7a h\u00ecnh c\u1ea7u trong \u0111\u1ec1 b\u00e0i tr\u00ean th\u00ec b\u1ea1n l\u1ea5y \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u01b0\u1eddng k\u00ednh \u0111\u1ec3 thay cho c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u l\u00e0 \u03c0 x d^2 v\u00e0 \u0111\u01b0\u1ee3c:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Di\u1ec7n t\u00edch = 3,14 x (2,5)^2 = 19,625 (cm2)<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299672 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-9.jpg\" alt=\"the-tich-khoi-cau-9\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 3<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: Cho 1 h\u00ecnh c\u1ea7u v\u1edbi \u0111\u01b0\u1eddng k\u00ednh l\u00e0 6cm. T\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ec d = 6cm n\u00ean suy ra b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u = d\/2 = 3cm<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u1eady S c\u1ee7a m\u1eb7t c\u1ea7u tr\u00ean l\u00e0 4 x \u03c0 x R^2 = 4 x \u03c0 x 3^2 = 36\u03c0 (cm2)<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 4<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: H\u00e3y t\u00ednh V kh\u1ed1i c\u1ea7u c\u00f3 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng k\u00ednh l\u00e0 4cm?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">r = d\/2 = 2cm<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u1eady th\u00ec V c\u1ee7a kh\u1ed1i c\u1ea7u = 4\/3 x \u03c0 x r^3 = 4\/3 x 3,14 x 2^3 = 33,49 (cm3)<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 5<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: Cho s\u1eb5n 1 m\u1eb7t c\u1ea7u c\u00f3 V l\u00e0 288\u03c0 cm3. V\u1eady \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u b\u1eb1ng bao nhi\u00eau?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u00ec V = 4\/3 x \u03c0 x r^3 = 288\u03c0 n\u00ean suy ra b\u00e1n k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u = 6cm.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Suy ra \u0111\u01b0\u1eddng k\u00ednh = 2r = 2 x 6 = 12 cm\u00a0<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 6<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: Cho 2 m\u1eb7t c\u1ea7u v\u1edbi d l\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng 1,5cm. B\u1ea1n h\u00e3y t\u00ednh V c\u1ee7a m\u1eb7t c\u1ea7u?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u01b0\u1eddng k\u00ednh = 1,5cm n\u00ean suy ra R = 0,75 cm v\u00e0 c\u1ee5 th\u1ec3 l\u00e0 b\u1eb1ng 7,5 x (10)^-3 (m)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">V\u1eady th\u00ec th\u1ec3 t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u = 1\/3 x \u03c0 x R^3 = \u2153 x \u03c0 x (7,5 x 10^-3)^3 = 4,42 x 10^-6 (m3)<\/span><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 7<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: H\u00e3y t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u ngo\u1ea1i ti\u1ebfp v\u1edbi h\u00ecnh h\u1ecdc l\u1eadp ph\u01b0\u01a1ng ABCD.EFGH c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ea1nh b\u1eb1ng 3cm?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n: G\u1ecdi b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u ngo\u1ea1i ti\u1ebfp v\u1edbi h\u00ecnh h\u1ecdc l\u1eadp ph\u01b0\u01a1ng l\u00e0 R. Nh\u01b0 v\u1eady ta c\u00f3 c\u1ea1nh CE = AB x \u221a3 = 3\u221a3 (cm).\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3 suy ra b\u00e1n k\u00ednh = 1\/2 CE = (3\u221a3)\/2 (cm)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nh\u01b0 v\u1eady th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u = V = 4\/3 x \u03c0 x R^3 = 4\/3 x \u03c0 x\u00a0 ((3\u221a3)\/2))^3 = (27\u221a3)\/2 x \u03c0 (cm3)<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299670 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-7.jpg\" alt=\"the-tich-khoi-cau-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3><span style=\"font-weight: 400;\">B\u00e0i t\u1eadp 8<\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0110\u1ec1 b\u00e0i: Cho m\u1ed9t kh\u1ed1i ch\u00f3p c\u00f3 t\u00ean l\u00e0 S.ABC v\u1edbi \u0111\u00e1y l\u00e0 1 tam gi\u00e1c vu\u00f4ng \u1edf A. C\u1ea1nh SA \u22a5 (ABC) v\u00e0 AB = b, SA = a, AC = c. M\u1ed9t m\u1eb7t c\u1ea7u \u0111i ngang qua nh\u1eefng \u0111\u1ecbnh S, A, C, B c\u00f3 \u0111\u1ed9 d\u00e0i b\u00e1n k\u00ednh l\u00e0 bao nhi\u00eau?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0110\u00e1p \u00e1n:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ta g\u1ecdi trung \u0111i\u1ec3m thu\u1ed9c c\u1ea1nh BC l\u00e0 \u0111i\u1ec3m M. L\u00fac n\u00e0y th\u00ec MA = MB = MC. Suy ra M ch\u00ednh l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 ngo\u1ea1i ti\u1ebfp v\u1edbi tam gi\u00e1c ABC nh\u01b0 h\u00ecnh.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-299671 aligncenter webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-8.jpg\" alt=\"the-tich-khoi-cau-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><span style=\"font-weight: 400;\">Sau \u0111\u00f3 ta d\u1ef1ng cho \u0111\u01b0\u1eddng Mt vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng ABC v\u00e0 ta \u0111\u01b0\u1ee3c Mt song song v\u1edbi c\u1ea1nh SA v\u00e0 Mt c\u0169ng ch\u00ednh l\u00e0 tr\u1ee5c c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 ngo\u1ea1i ti\u1ebfp v\u1edbi tam gi\u00e1c ABC.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Trong m\u1eb7t ph\u1eb3ng \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi c\u1ea1nh SA v\u00e0 Mt th\u00ec \u0111\u01b0\u1eddng trung tr\u1ef1c thu\u1ed9c SA s\u1ebd c\u1eaft \u0111\u01b0\u1eddng Mt \u1edf \u0111i\u1ec3m I. Ta \u0111\u01b0\u1ee3c:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">IA = IS v\u00e0 IC = IB = IA<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">T\u1eeb \u0111\u00f3 suy ra IA = IB = IC = IS<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Suy ra I ch\u00ednh t\u00e2m c\u1ee7a m\u1eb7t c\u1ea7u c\u00f3 ngo\u1ea1i ti\u1ebfp v\u1edbi t\u1ee9 di\u1ec7n t\u00ean S.ABC.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">V\u1eady th\u00ec b\u00e1n k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u l\u00e0: R = IA = \u221aAM^2 + MI^2. Trong \u0111\u00f3:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">AM = BC\/2 = 1\/2 \u221aAB^2 + AC^2 = 1\/2 \u221ab^2 + c^2<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">MI = SA\/2 = a\/2<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Suy ra b\u00e1n k\u00ednh = \u221a((b^2 + c^2)\/4) + (a^2\/4 ) = 1\/2 \u221aa^2 + b^2 + c^2<\/span><\/li>\n<\/ul>\n<h2><span style=\"font-weight: 400;\">M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u, di\u1ec7n t\u00edch kh\u1ed1i c\u1ea7u t\u1ef1 luy\u1ec7n<\/span><\/h2>\n<p><span style=\"font-weight: 400;\">Sau \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp t\u00ednh th\u1ec3 t\u00edch, di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u t\u1ef1 luy\u1ec7n m\u00e0 c\u00e1c b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u00e0i 1: Cho 1 m\u1eb7t c\u1ea7u S g\u1ed3m b\u00e1n k\u00ednh l\u00e0 r v\u00e0 1 m\u1eb7t c\u1ea7u S\u2019 g\u1ed3m b\u00e1n k\u00ednh l\u00e0 r\u2019. Bi\u1ebft r\u1eb1ng r\u2019 = 2r. V\u1eady t\u1ec9 s\u1ed1 v\u1ec1 di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u S\u2019 v\u00e0 S l\u00e0 bao nhi\u00eau?<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> S = 1\/2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 1\/3<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 4<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">B\u00e0i 2: Cho kh\u1ed1i c\u1ea7u c\u00f3 b\u00e1n k\u00ednh l\u00e0 r, di\u1ec7n t\u00edch l\u00e0 S v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u l\u00e0 V. V\u1eady sau \u0111\u00e2y c\u00f4ng th\u1ee9c n\u00e0o \u0111\u00e3 l\u1eadp sai?<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> S = \u03c0r^2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 4\u03c0r^2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 2\u03c0r^2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 4\/3\u03c0r^2<\/span><\/li>\n<\/ol>\n<figure id=\"attachment_299673\" aria-describedby=\"caption-attachment-299673\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-10-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/the-tich-khoi-cau-10-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-299673 size-full webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-10.jpg\" alt=\"the-tich-khoi-cau-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/the-tich-khoi-cau-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><figcaption id=\"caption-attachment-299673\" class=\"wp-caption-text\">M\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u, di\u1ec7n t\u00edch kh\u1ed1i c\u1ea7u t\u1ef1 luy\u1ec7n<\/figcaption><\/figure>\n<p><span style=\"font-weight: 400;\">B\u00e0i 3: Cho 1 h\u00ecnh c\u1ea7u c\u00f3 r l\u00e0 b\u00e1n k\u00ednh. V\u1eady S c\u1ee7a m\u1eb7t c\u1ea7u l\u00e0?<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> S = 4\u03c0r^2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 6\u03c0r^2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = 2\u03c0r^2<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = \u03c0r^2<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">B\u00e0i 4: Cho 1 h\u00ecnh c\u1ea7u c\u00f3 r l\u00e0 b\u00e1n k\u00ednh. L\u00fac \u0111\u00f3 th\u00ec V c\u1ee7a h\u00ecnh c\u1ea7u s\u1ebd l\u00e0?<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> S = (4\u03c0r^2)\/3<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = (3\u03c0r^3)\/4<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = (4\u03c0r^3)\/3<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> S = (2\u03c0r^3)\/3<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">B\u00e0i 5: Cho 1 t\u1ee9 di\u1ec7n ABCD \u0111\u1ec1u v\u1edbi c\u1ea1nh \u0111\u00e1y c\u00f3 \u0111\u1ed9 d\u00e0i l\u00e0 a. H\u00e3y t\u00ednh V h\u00ecnh c\u1ea7u c\u00f3 ngo\u1ea1i ti\u1ebfp v\u1edbi t\u1ee9 di\u1ec7n n\u00e0y?<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> (\u03c0a^3\u221a6)\/8<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> (\u03c0a^3\u221a6)\/6<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> (\u03c0a^3\u221a6)\/4<\/span><\/li>\n<li><span style=\"font-weight: 400;\"> (3\u03c0a^3\u221a6)\/8<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">B\u00e0i vi\u1ebft tr\u00ean \u0111\u00e3 chia s\u1ebb chi ti\u1ebft v\u1ec1 h\u00ecnh c\u1ea7u v\u00e0 c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u, di\u1ec7n t\u00edch kh\u1ed1i c\u1ea7u cho m\u1ecdi ng\u01b0\u1eddi t\u00ecm hi\u1ec3u. Hy v\u1ecdng c\u00e1c b\u1ea1n h\u1ecdc sinh s\u1ebd n\u1eafm r\u00f5 c\u00e1c c\u00f4ng th\u1ee9c tr\u00ean v\u00e0 c\u00e1ch gi\u1ea3i b\u00e0i t\u1eadp nhanh ch\u00f3ng. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c gi\u00fap b\u1ea1n h\u1ecdc t\u1ed1t h\u01a1n m\u00f4n h\u00ecnh h\u1ecdc \u1edf l\u1edbp.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Tham kh\u1ea3o b\u00e0i vi\u1ebft li\u00ean quan:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-nguyen-to-la-gi\/\"><span style=\"font-weight: 400;\">S\u1ed1 nguy\u00ean t\u1ed1 l\u00e0 g\u00ec? V\u00ed d\u1ee5 minh h\u1ecda, t\u00ednh ch\u1ea5t, b\u1ea3ng s\u1ed1 nguy\u00ean t\u1ed1<\/span><\/a><\/li>\n<li style=\"font-weight: 400;\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/trong-tam-la-gi\/\"><span style=\"font-weight: 400;\">T\u00ednh ch\u1ea5t c\u1ee7a tr\u1ecdng t\u00e2m v\u00e0 c\u00e1ch x\u00e1c \u0111\u1ecbnh tr\u1ecdng t\u00e2m tam gi\u00e1c trong H\u00ecnh h\u1ecdc<\/span><\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u l\u00e0 ki\u1ebfn th\u1ee9c m\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea7n ph\u1ea3i n\u1eafm v\u1eefng \u0111\u1ec3 chu\u1ea9n b\u1ecb cho nh\u1eefng k\u1ef3 thi s\u1eafp \u0111\u1ebfn. Vi\u1ec7c n\u1eafm r\u00f5 c\u00f4ng th\u1ee9c n\u00e0y c\u0169ng gi\u00fap b\u1ea1n \u00f4n thi v\u00e0 l\u00e0m b\u00e0i t\u1eadp nhanh ch\u00f3ng h\u01a1n. N\u1ebfu c\u00e1c b\u1ea1n v\u1eabn [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":299663,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-299661","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u v\u00e0 di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/title>\n<meta name=\"description\" content=\"C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u, di\u1ec7n t\u00edch kh\u1ed1i c\u1ea7u l\u00e0 ki\u1ebfn th\u1ee9c m\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea7n n\u1eafm r\u00f5 \u0111\u1ec3 h\u1ecdc t\u1ed1t m\u00f4n h\u00ecnh 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