{"id":567144,"date":"2026-07-22T11:39:06","date_gmt":"2026-07-22T04:39:06","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567144"},"modified":"2026-07-22T11:39:06","modified_gmt":"2026-07-22T04:39:06","slug":"the-tich-hinh-non","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-hinh-non\/","title":{"rendered":"Th\u1ec3 t\u00edch h\u00ecnh n\u00f3n: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 t\u00ednh chi ti\u1ebft"},"content":{"rendered":"<p>Th\u1ec3 t\u00edch h\u00ecnh n\u00f3n l\u00e0 c\u00f4ng th\u1ee9c h\u00ecnh h\u1ecdc kh\u00f4ng gian quen thu\u1ed9c trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n THCS, v\u1eabn xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u \u0111\u1ec1 \u00f4n thi v\u00e0o 10 v\u00e0 b\u00e0i t\u1eadp \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. Nhi\u1ec1u b\u1ea1n nh\u1edb c\u00f4ng th\u1ee9c V = 1\/3 \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h nh\u01b0ng d\u1ec5 nh\u1ea7m khi \u0111\u1ec1 ch\u1ec9 cho \u0111\u01b0\u1eddng sinh, ho\u1eb7c l\u1eabn gi\u1eefa di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n. N\u1ed9i dung sau t\u1ed5ng h\u1ee3p c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh n\u00f3n, c\u00e1ch t\u00ednh \u0111\u01b0\u1eddng sinh v\u00e0 di\u1ec7n t\u00edch, k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc, b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng v\u00e0 ph\u1ea7n h\u1ecfi \u0111\u00e1p nhanh \u0111\u1ec3 b\u1ea1n tra c\u1ee9u khi \u00f4n t\u1eadp.<\/p>\n<h2>H\u00ecnh n\u00f3n l\u00e0 g\u00ec?<\/h2>\n<p>H\u00ecnh n\u00f3n l\u00e0 kh\u1ed1i tr\u00f2n xoay \u0111\u01b0\u1ee3c t\u1ea1o ra khi quay m\u1ed9t tam gi\u00e1c vu\u00f4ng m\u1ed9t v\u00f2ng quanh m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng c\u1ed1 \u0111\u1ecbnh, c\u1ea1nh \u0111\u00f3 tr\u1edf th\u00e0nh tr\u1ee5c v\u00e0 c\u0169ng l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh n\u00f3n.<\/p>\n<p>M\u1ed9t h\u00ecnh n\u00f3n g\u1ed3m ba y\u1ebfu t\u1ed1 ch\u00ednh: \u0111\u00e1y l\u00e0 h\u00ecnh tr\u00f2n b\u00e1n k\u00ednh r, \u0111\u1ec9nh l\u00e0 \u0111i\u1ec3m cao nh\u1ea5t, v\u00e0 \u0111\u01b0\u1eddng sinh l n\u1ed1i \u0111\u1ec9nh v\u1edbi m\u1ed9t \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y. Chi\u1ec1u cao h l\u00e0 kho\u1ea3ng c\u00e1ch vu\u00f4ng g\u00f3c t\u1eeb \u0111\u1ec9nh xu\u1ed1ng t\u00e2m \u0111\u00e1y. Ba \u0111\u1ea1i l\u01b0\u1ee3ng r, h, l li\u00ean h\u1ec7 v\u1edbi nhau qua \u0111\u1ecbnh l\u00fd Pythagore v\u00ec t\u1ea1o th\u00e0nh m\u1ed9t tam gi\u00e1c vu\u00f4ng.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-568844 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-1.jpg\" alt=\"the-tich-hinh-non-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh n\u00f3n<\/h2>\n<p>Th\u1ec3 t\u00edch kh\u1ed1i n\u00f3n b\u1eb1ng m\u1ed9t ph\u1ea7n ba t\u00edch c\u1ee7a di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 chi\u1ec1u cao, \u0111\u00fang b\u1eb1ng c\u00f4ng th\u1ee9c m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 \u0111\u00e3 h\u1ecdc \u1edf l\u1edbp 9.<\/p>\n<p><strong>V = (1\/3) \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h<\/strong><\/p>\n<p>Trong \u0111\u00f3 r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao n\u1ed1i t\u1eeb \u0111\u1ec9nh xu\u1ed1ng t\u00e2m \u0111\u00e1y, \u03c0 x\u1ea5p x\u1ec9 3,14. C\u00f4ng th\u1ee9c n\u00e0y l\u00e0 d\u1ea1ng \u0111\u1eb7c bi\u1ec7t c\u1ee7a c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p (V = 1\/3 \u00d7 di\u1ec7n t\u00edch \u0111\u00e1y \u00d7 chi\u1ec1u cao), v\u00ec h\u00ecnh n\u00f3n c\u00f3 th\u1ec3 coi l\u00e0 h\u00ecnh ch\u00f3p v\u1edbi \u0111\u00e1y h\u00ecnh tr\u00f2n thay v\u00ec \u0111a gi\u00e1c.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0110\u1ea1i l\u01b0\u1ee3ng<\/th>\n<th>K\u00fd hi\u1ec7u<\/th>\n<th>\u00dd ngh\u0129a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>B\u00e1n k\u00ednh \u0111\u00e1y<\/td>\n<td>r<\/td>\n<td>Kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u00e1y \u0111\u1ebfn m\u00e9p \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y<\/td>\n<\/tr>\n<tr>\n<td>Chi\u1ec1u cao<\/td>\n<td>h<\/td>\n<td>Kho\u1ea3ng c\u00e1ch vu\u00f4ng g\u00f3c t\u1eeb \u0111\u1ec9nh xu\u1ed1ng t\u00e2m \u0111\u00e1y<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u01b0\u1eddng sinh<\/td>\n<td>l<\/td>\n<td>\u0110o\u1ea1n n\u1ed1i \u0111\u1ec9nh v\u1edbi m\u1ed9t \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00e1y<\/td>\n<\/tr>\n<tr>\n<td>Th\u1ec3 t\u00edch<\/td>\n<td>V<\/td>\n<td>V = (1\/3) \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" class=\"size-full wp-image-568845 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-2.jpg\" alt=\"the-tich-hinh-non-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u0110\u01b0\u1eddng sinh, di\u1ec7n t\u00edch xung quanh v\u00e0 to\u00e0n ph\u1ea7n<\/h2>\n<p>Ngo\u00e0i th\u1ec3 t\u00edch, \u0111\u1ec1 b\u00e0i th\u01b0\u1eddng y\u00eau c\u1ea7u t\u00ednh th\u00eam \u0111\u01b0\u1eddng sinh, di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n \u2014 ba \u0111\u1ea1i l\u01b0\u1ee3ng n\u00e0y \u0111\u1ec1u t\u00ednh \u0111\u01b0\u1ee3c khi bi\u1ebft r v\u00e0 h.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0110\u1ea1i l\u01b0\u1ee3ng<\/th>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0110\u01b0\u1eddng sinh (l)<\/td>\n<td>l = \u221a(r\u00b2 + h\u00b2)<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch xung quanh (Sxq)<\/td>\n<td>Sxq = \u03c0 \u00d7 r \u00d7 l<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch \u0111\u00e1y (S\u0111\u00e1y)<\/td>\n<td>S\u0111\u00e1y = \u03c0 \u00d7 r\u00b2<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n (Stp)<\/td>\n<td>Stp = Sxq + S\u0111\u00e1y = \u03c0 \u00d7 r \u00d7 l + \u03c0 \u00d7 r\u00b2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0110\u01b0\u1eddng sinh suy ra tr\u1ef1c ti\u1ebfp t\u1eeb \u0111\u1ecbnh l\u00fd Pythagore v\u00ec r, h v\u00e0 l t\u1ea1o th\u00e0nh tam gi\u00e1c vu\u00f4ng. Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n lu\u00f4n l\u1edbn h\u01a1n di\u1ec7n t\u00edch xung quanh v\u00ec c\u1ed9ng th\u00eam ph\u1ea7n \u0111\u00e1y, do h\u00ecnh n\u00f3n ch\u1ec9 c\u00f3 m\u1ed9t m\u1eb7t \u0111\u00e1y \u2014 kh\u00e1c h\u00ecnh tr\u1ee5 c\u00f3 hai \u0111\u00e1y.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-568846 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-3.jpg\" alt=\"the-tich-hinh-non-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 t\u00ednh th\u1ec3 t\u00edch h\u00ecnh n\u00f3n<\/h2>\n<p>C\u00f9ng \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean v\u00e0o m\u1ed9t b\u00e0i to\u00e1n c\u1ee5 th\u1ec3 \u0111\u1ec3 b\u1ea1n h\u00ecnh dung r\u00f5 c\u00e1ch thay s\u1ed1.<\/p>\n<p><strong>\u0110\u1ec1 b\u00e0i:<\/strong> M\u1ed9t h\u00ecnh n\u00f3n c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r = 3cm, chi\u1ec1u cao h = 4cm. T\u00ednh \u0111\u01b0\u1eddng sinh, th\u1ec3 t\u00edch, di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00f3n.<\/p>\n<p><strong>L\u1eddi gi\u1ea3i:<\/strong><\/p>\n<p><strong>B\u01b0\u1edbc 1 \u2014 T\u00ednh \u0111\u01b0\u1eddng sinh:<\/strong> l = \u221a(r\u00b2 + h\u00b2) = \u221a(3\u00b2 + 4\u00b2) = \u221a(9 + 16) = \u221a25 = 5cm.<\/p>\n<p><strong>B\u01b0\u1edbc 2 \u2014 T\u00ednh th\u1ec3 t\u00edch:<\/strong> V = (1\/3) \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h = (1\/3) \u00d7 3,14 \u00d7 9 \u00d7 4 = (1\/3) \u00d7 113,04 \u2248 37,68cm\u00b3.<\/p>\n<p><strong>B\u01b0\u1edbc 3 \u2014 T\u00ednh di\u1ec7n t\u00edch xung quanh:<\/strong> Sxq = \u03c0 \u00d7 r \u00d7 l = 3,14 \u00d7 3 \u00d7 5 = 47,1cm\u00b2.<\/p>\n<p><strong>B\u01b0\u1edbc 4 \u2014 T\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n:<\/strong> Stp = Sxq + \u03c0 \u00d7 r\u00b2 = 47,1 + 3,14 \u00d7 9 = 47,1 + 28,26 = 75,36cm\u00b2.<\/p>\n<p>V\u1eady h\u00ecnh n\u00f3n n\u00e0y c\u00f3 \u0111\u01b0\u1eddng sinh 5cm, th\u1ec3 t\u00edch kho\u1ea3ng 37,68cm\u00b3, di\u1ec7n t\u00edch xung quanh 47,1cm\u00b2 v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n 75,36cm\u00b2.<\/p>\n<h2>B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p>B\u1ea1n th\u1eed \u00e1p d\u1ee5ng \u0111\u00fang b\u1ed1n b\u01b0\u1edbc \u1edf tr\u00ean v\u1edbi s\u1ed1 li\u1ec7u kh\u00e1c \u0111\u1ec3 t\u1ef1 ki\u1ec3m tra m\u1ee9c \u0111\u1ed9 n\u1eafm b\u00e0i.<\/p>\n<p><strong>\u0110\u1ec1 b\u00e0i:<\/strong> M\u1ed9t h\u00ecnh n\u00f3n c\u00f3 b\u00e1n k\u00ednh \u0111\u00e1y r = 5cm, chi\u1ec1u cao h = 12cm. T\u00ednh \u0111\u01b0\u1eddng sinh, th\u1ec3 t\u00edch, di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n.<\/p>\n<p><strong>L\u1eddi gi\u1ea3i:<\/strong><\/p>\n<p>\u0110\u01b0\u1eddng sinh: l = \u221a(5\u00b2 + 12\u00b2) = \u221a(25 + 144) = \u221a169 = 13cm.<\/p>\n<p>Th\u1ec3 t\u00edch: V = (1\/3) \u00d7 3,14 \u00d7 5\u00b2 \u00d7 12 = (1\/3) \u00d7 3,14 \u00d7 300 = (1\/3) \u00d7 942 = 314cm\u00b3.<\/p>\n<p>Di\u1ec7n t\u00edch xung quanh: Sxq = 3,14 \u00d7 5 \u00d7 13 = 204,1cm\u00b2.<\/p>\n<p>Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n: Stp = 204,1 + 3,14 \u00d7 25 = 204,1 + 78,5 = 282,6cm\u00b2.<\/p>\n<p>K\u1ebft qu\u1ea3: \u0111\u01b0\u1eddng sinh 13cm, th\u1ec3 t\u00edch 314cm\u00b3, di\u1ec7n t\u00edch xung quanh 204,1cm\u00b2 v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n 282,6cm\u00b2 \u2014 b\u1ed9 s\u1ed1 Pythagore quen thu\u1ed9c (5-12-13) hay g\u1eb7p trong \u0111\u1ec1 ki\u1ec3m tra.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568847 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-4.jpg\" alt=\"the-tich-hinh-non-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>H\u00ecnh n\u00f3n c\u1ee5t v\u00e0 c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch<\/h2>\n<p>H\u00ecnh n\u00f3n c\u1ee5t l\u00e0 ph\u1ea7n c\u00f2n l\u1ea1i c\u1ee7a h\u00ecnh n\u00f3n sau khi c\u1eaft b\u1ecf ph\u1ea7n ch\u00f3p nh\u1ecf ph\u00eda tr\u00ean b\u1eb1ng m\u1ed9t m\u1eb7t ph\u1eb3ng song song v\u1edbi \u0111\u00e1y, t\u1ea1o ra hai \u0111\u00e1y h\u00ecnh tr\u00f2n v\u1edbi b\u00e1n k\u00ednh kh\u00e1c nhau.<\/p>\n<p>C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n c\u1ee5t:<\/p>\n<p><strong>V = (1\/3) \u00d7 \u03c0 \u00d7 h \u00d7 (R\u00b2 + R\u00d7r + r\u00b2)<\/strong><\/p>\n<p>Trong \u0111\u00f3 R l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y l\u1edbn, r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y nh\u1ecf, h l\u00e0 chi\u1ec1u cao gi\u1eefa hai \u0111\u00e1y. Khi r ti\u1ebfn v\u1ec1 0, c\u00f4ng th\u1ee9c quay l\u1ea1i \u0111\u00fang c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n th\u00f4ng th\u01b0\u1eddng \u2014 c\u00e1ch nhi\u1ec1u b\u1ea1n d\u00f9ng \u0111\u1ec3 ki\u1ec3m tra l\u1ea1i c\u00f4ng th\u1ee9c khi kh\u00f4ng nh\u1edb ch\u00ednh x\u00e1c.<\/p>\n<h2>C\u00e1c b\u01b0\u1edbc gi\u1ea3i b\u00e0i to\u00e1n h\u00ecnh n\u00f3n nhanh, ch\u00ednh x\u00e1c<\/h2>\n<p>Ph\u1ea7n l\u1edbn l\u1ed7i sai khi l\u00e0m b\u00e0i kh\u00f4ng \u0111\u1ebfn t\u1eeb vi\u1ec7c qu\u00ean c\u00f4ng th\u1ee9c m\u00e0 t\u1eeb vi\u1ec7c thay s\u1ed1 nh\u1ea7m ho\u1eb7c b\u1ecf s\u00f3t b\u01b0\u1edbc trung gian.<\/p>\n<ul>\n<li>\u0110\u1ecdc k\u1ef9 \u0111\u1ec1 \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u00e3 cho l\u00e0 r, h hay l tr\u01b0\u1edbc khi thay v\u00e0o c\u00f4ng th\u1ee9c.<\/li>\n<li>V\u1ebd tam gi\u00e1c vu\u00f4ng r-h-l \u0111\u1ec3 tr\u00e1nh nh\u1ea7m c\u1ea1nh khi \u00e1p d\u1ee5ng Pythagore.<\/li>\n<li>Gi\u1eef nguy\u00ean ph\u00e2n s\u1ed1 1\/3 \u0111\u1ebfn b\u01b0\u1edbc cu\u1ed1i \u0111\u1ec3 tr\u00e1nh sai s\u1ed1 l\u00e0m tr\u00f2n.<\/li>\n<li>Ki\u1ec3m tra \u0111\u01a1n v\u1ecb: \u0111\u1ec1 cho cm th\u00ec th\u1ec3 t\u00edch l\u00e0 cm\u00b3, di\u1ec7n t\u00edch l\u00e0 cm\u00b2. V\u1edbi h\u00ecnh n\u00f3n c\u1ee5t, x\u00e1c \u0111\u1ecbnh \u0111\u00fang \u0111\u00e1y R (l\u1edbn) v\u00e0 r (nh\u1ecf) tr\u01b0\u1edbc khi t\u00ednh.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-568848 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-5.jpg\" alt=\"the-tich-hinh-non-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/the-tich-hinh-non-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Ph\u00e2n bi\u1ec7t h\u00ecnh n\u00f3n v\u00e0 h\u00ecnh ch\u00f3p<\/h2>\n<p>H\u00ecnh n\u00f3n v\u00e0 h\u00ecnh ch\u00f3p d\u00f9ng chung d\u1ea1ng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch nh\u01b0ng kh\u00e1c nhau \u1edf h\u00ecnh d\u1ea1ng \u0111\u00e1y v\u00e0 m\u1eb7t b\u00ean.<\/p>\n<table>\n<thead>\n<tr>\n<th>Ti\u00eau ch\u00ed<\/th>\n<th>H\u00ecnh n\u00f3n<\/th>\n<th>H\u00ecnh ch\u00f3p<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0110\u00e1y<\/td>\n<td>H\u00ecnh tr\u00f2n<\/td>\n<td>\u0110a gi\u00e1c (tam gi\u00e1c, t\u1ee9 gi\u00e1c&#8230;)<\/td>\n<\/tr>\n<tr>\n<td>M\u1eb7t b\u00ean<\/td>\n<td>M\u1ed9t m\u1eb7t cong duy nh\u1ea5t<\/td>\n<td>Nhi\u1ec1u m\u1eb7t tam gi\u00e1c ph\u1eb3ng<\/td>\n<\/tr>\n<tr>\n<td>C\u1ea1nh n\u1ed1i \u0111\u1ec9nh v\u1edbi \u0111\u00e1y<\/td>\n<td>\u0110\u01b0\u1eddng sinh (v\u00f4 s\u1ed1, b\u1eb1ng nhau)<\/td>\n<td>C\u00e1c c\u1ea1nh b\u00ean (s\u1ed1 l\u01b0\u1ee3ng b\u1eb1ng s\u1ed1 c\u1ea1nh \u0111\u00e1y)<\/td>\n<\/tr>\n<tr>\n<td>C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch<\/td>\n<td>V = (1\/3) \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h<\/td>\n<td>V = (1\/3) \u00d7 S\u0111\u00e1y \u00d7 h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>N\u1ebfu c\u1ea7n \u00f4n th\u00eam kh\u1ed1i \u0111a di\u1ec7n, b\u1ea1n c\u00f3 th\u1ec3 tham kh\u1ea3o c\u00e1ch t\u00ednh <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-hinh-hop-chu-nhat\/\">th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt<\/a> ho\u1eb7c <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/hinh-lang-tru-dung\/\">h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng<\/a> \u2014 hai d\u1ea1ng kh\u1ed1i c\u01a1 b\u1ea3n hay xu\u1ea5t hi\u1ec7n c\u00f9ng chuy\u00ean \u0111\u1ec1 v\u1edbi h\u00ecnh n\u00f3n.<\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 th\u1ec3 t\u00edch h\u00ecnh n\u00f3n<\/h2>\n<h3>1. C\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh n\u00f3n l\u00e0 g\u00ec?<\/h3>\n<p>Th\u1ec3 t\u00edch h\u00ecnh n\u00f3n t\u00ednh theo c\u00f4ng th\u1ee9c V = (1\/3) \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h, v\u1edbi r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao, \u03c0 x\u1ea5p x\u1ec9 3,14.<\/p>\n<h3>2. \u0110\u01b0\u1eddng sinh c\u1ee7a h\u00ecnh n\u00f3n t\u00ednh nh\u01b0 th\u1ebf n\u00e0o?<\/h3>\n<p>\u0110\u01b0\u1eddng sinh l = \u221a(r\u00b2 + h\u00b2), \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pythagore cho tam gi\u00e1c vu\u00f4ng t\u1ea1o b\u1edfi b\u00e1n k\u00ednh \u0111\u00e1y, chi\u1ec1u cao v\u00e0 \u0111\u01b0\u1eddng sinh.<\/p>\n<h3>3. Di\u1ec7n t\u00edch xung quanh h\u00ecnh n\u00f3n t\u00ednh ra sao?<\/h3>\n<p>Di\u1ec7n t\u00edch xung quanh Sxq = \u03c0 \u00d7 r \u00d7 l, v\u1edbi r l\u00e0 b\u00e1n k\u00ednh \u0111\u00e1y v\u00e0 l l\u00e0 \u0111\u01b0\u1eddng sinh.<\/p>\n<h3>4. Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n h\u00ecnh n\u00f3n g\u1ed3m nh\u1eefng ph\u1ea7n n\u00e0o?<\/h3>\n<p>Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n Stp = \u03c0 \u00d7 r \u00d7 l + \u03c0 \u00d7 r\u00b2, b\u1eb1ng di\u1ec7n t\u00edch xung quanh c\u1ed9ng di\u1ec7n t\u00edch \u0111\u00e1y.<\/p>\n<h3>5. H\u00ecnh n\u00f3n c\u1ee5t c\u00f3 c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch kh\u00e1c h\u00ecnh n\u00f3n th\u01b0\u1eddng kh\u00f4ng?<\/h3>\n<p>C\u00f3. Th\u1ec3 t\u00edch h\u00ecnh n\u00f3n c\u1ee5t: V = (1\/3) \u00d7 \u03c0 \u00d7 h \u00d7 (R\u00b2 + R\u00d7r + r\u00b2), v\u1edbi R, r l\u00e0 b\u00e1n k\u00ednh hai \u0111\u00e1y, h l\u00e0 chi\u1ec1u cao gi\u1eefa hai \u0111\u00e1y.<\/p>\n<h3>6. V\u00ec sao th\u1ec3 t\u00edch h\u00ecnh n\u00f3n b\u1eb1ng 1\/3 th\u1ec3 t\u00edch h\u00ecnh tr\u1ee5 c\u00f9ng \u0111\u00e1y, c\u00f9ng chi\u1ec1u cao?<\/h3>\n<p>\u0110\u00e2y l\u00e0 k\u1ebft qu\u1ea3 h\u00ecnh h\u1ecdc \u0111\u00e3 ch\u1ee9ng minh: v\u1edbi c\u00f9ng b\u00e1n k\u00ednh \u0111\u00e1y v\u00e0 chi\u1ec1u cao, kh\u1ed1i n\u00f3n lu\u00f4n b\u1eb1ng m\u1ed9t ph\u1ea7n ba th\u1ec3 t\u00edch kh\u1ed1i tr\u1ee5 t\u01b0\u01a1ng \u1ee9ng.<\/p>\n<h3>7. L\u00e0m sao nh\u1edb nhanh c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n khi l\u00e0m b\u00e0i thi?<\/h3>\n<p>B\u1ea1n c\u00f3 th\u1ec3 nh\u1edb th\u1ec3 t\u00edch h\u00ecnh n\u00f3n b\u1eb1ng 1\/3 di\u1ec7n t\u00edch \u0111\u00e1y nh\u00e2n chi\u1ec1u cao, t\u01b0\u01a1ng t\u1ef1 c\u00f4ng th\u1ee9c h\u00ecnh ch\u00f3p v\u00ec h\u00ecnh n\u00f3n l\u00e0 h\u00ecnh ch\u00f3p c\u00f3 \u0111\u00e1y tr\u00f2n.<\/p>\n<h3>8. Khi t\u00ednh th\u1ec3 t\u00edch h\u00ecnh n\u00f3n c\u1ea7n l\u01b0u \u00fd g\u00ec v\u1ec1 \u0111\u01a1n v\u1ecb?<\/h3>\n<p>B\u00e1n k\u00ednh v\u00e0 chi\u1ec1u cao c\u1ea7n c\u00f9ng \u0111\u01a1n v\u1ecb tr\u01b0\u1edbc khi thay v\u00e0o c\u00f4ng th\u1ee9c; k\u1ebft qu\u1ea3 th\u1ec3 t\u00edch c\u00f3 \u0111\u01a1n v\u1ecb kh\u1ed1i t\u01b0\u01a1ng \u1ee9ng, v\u00ed d\u1ee5 cm\u00b3 ho\u1eb7c m\u00b3.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>N\u1eafm v\u1eefng c\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n V = (1\/3) \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h c\u00f9ng c\u00e1ch t\u00ednh \u0111\u01b0\u1eddng sinh, di\u1ec7n t\u00edch xung quanh v\u00e0 to\u00e0n ph\u1ea7n s\u1ebd gi\u00fap b\u1ea1n x\u1eed l\u00fd g\u1ecdn c\u00e1c d\u1ea1ng b\u00e0i t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, k\u1ec3 c\u1ea3 h\u00ecnh n\u00f3n c\u1ee5t. B\u1ea1n c\u00f3 th\u1ec3 luy\u1ec7n th\u00eam d\u1ea1ng b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/hinh-chieu\/\">h\u00ecnh chi\u1ebfu<\/a> \u0111\u1ec3 c\u1ee7ng c\u1ed1 kh\u1ea3 n\u0103ng \u0111\u1ecdc h\u00ecnh tr\u01b0\u1edbc khi gi\u1ea3i to\u00e1n. 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Nhi\u1ec1u b\u1ea1n nh\u1edb c\u00f4ng th\u1ee9c V = 1\/3 \u00d7 \u03c0 \u00d7 r\u00b2 \u00d7 h nh\u01b0ng d\u1ec5 nh\u1ea7m khi \u0111\u1ec1 ch\u1ec9 [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":568841,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"th\u1ec3 t\u00edch h\u00ecnh n\u00f3n","_yoast_wpseo_title":"Th\u1ec3 t\u00edch h\u00ecnh n\u00f3n: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5","_yoast_wpseo_metadesc":"C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n chu\u1ea9n SGK: V = 1\/3\u03c0r\u00b2h, k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc, b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng v\u00e0 FAQ d\u1ec5 hi\u1ec3u. Xem chi ti\u1ebft t\u1ea1i Ho\u00e0ng H\u00e0 Mobile.","footnotes":""},"categories":[16],"tags":[],"class_list":["post-567144","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-thu-thuat"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Th\u1ec3 t\u00edch h\u00ecnh n\u00f3n: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5<\/title>\n<meta name=\"description\" content=\"C\u00f4ng th\u1ee9c th\u1ec3 t\u00edch h\u00ecnh n\u00f3n chu\u1ea9n SGK: V = 1\/3\u03c0r\u00b2h, k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc, b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng v\u00e0 FAQ d\u1ec5 hi\u1ec3u. 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