{"id":305786,"date":"2024-01-12T19:44:18","date_gmt":"2024-01-12T12:44:18","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=305786"},"modified":"2024-01-12T19:44:18","modified_gmt":"2024-01-12T12:44:18","slug":"dien-tich-hinh-cau","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-cau\/","title":{"rendered":"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u, th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u"},"content":{"rendered":"

B\u1ea1n chu\u1ea9n b\u1ecb cho k\u1ef3 thi s\u1eafp t\u1edbi nh\u01b0ng c\u1ea3m th\u1ea5y m\u01a1 h\u1ed3 v\u1edbi h\u00ecnh c\u1ea7u? C\u1ea3m gi\u00e1c kh\u00f4ng bi\u1ebft n\u00ean b\u1eaft \u0111\u1ea7u t\u1eeb \u0111\u00e2u khi t\u00ednh <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/b> v\u00e0 th\u1ec3 t\u00edch c\u1ee7a n\u00f3? \u0110\u1eebng lo l\u1eafng, h\u00ecnh c\u1ea7u c\u00f3 th\u1ec3 g\u00e2y kh\u00f3 kh\u0103n ban \u0111\u1ea7u, nh\u01b0ng th\u00f4ng qua c\u00e1c c\u00f4ng th\u1ee9c v\u00e0 c\u00e1ch t\u00ednh \u0111\u01a1n gi\u1ea3n, ch\u00fang ta s\u1ebd th\u1ea5y \u0111\u00f3 kh\u00f4ng ph\u1ea3i l\u00e0 nhi\u1ec7m v\u1ee5 kh\u00f3 kh\u0103n. H\u00e3y c\u00f9ng t\u00ecm hi\u1ec3u c\u00e1c c\u00e1ch t\u00ednh di\u1ec7n t\u00edch cho h\u00ecnh c\u1ea7u, m\u1ed9t ki\u1ebfn th\u1ee9c quan tr\u1ecdng trong h\u00ecnh h\u1ecdc kh\u00f4ng gian c\u1ea7n n\u1eafm \u0111\u1ec3 chu\u1ea9n b\u1ecb t\u1ed1t nh\u1ea5t cho k\u1ef3 thi s\u1eafp t\u1edbi c\u1ee7a b\u1ea1n.<\/span><\/p>\n

H\u00ecnh c\u1ea7u, m\u1eb7t c\u1ea7u l\u00e0 g\u00ec?<\/span><\/h2>\n

H\u00ecnh c\u1ea7u l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc quan tr\u1ecdng, m\u00f4 t\u1ea3 m\u1ed9t kh\u00f4ng gian ba chi\u1ec1u c\u00f3 h\u00ecnh d\u1ea1ng gi\u1ed1ng nh\u01b0 m\u1ed9t qu\u1ea3 c\u1ea7u, v\u1edbi \u0111i\u1ec3m trung t\u00e2m c\u1ed1 \u0111\u1ecbnh v\u00e0 c\u00e1c \u0111i\u1ec3m tr\u00ean b\u1ec1 m\u1eb7t c\u00e1ch nhau m\u1ed9t kho\u1ea3ng c\u00e1ch nh\u01b0 nhau. B\u1ec1 m\u1eb7t cong c\u1ee7a h\u00ecnh c\u1ea7u t\u1ea1o n\u00ean kh\u00f4ng gian li\u00ean t\u1ee5c, cong v\u00fat theo m\u1ecdi h\u01b0\u1edbng.<\/span><\/p>\n

\"dien-tich-hinh-cau-1\"<\/p>\n

M\u1eb7t c\u1ea7u l\u00e0 ph\u1ea7n c\u1ee7a b\u1ec1 m\u1eb7t h\u00ecnh c\u1ea7u, \u0111\u00f3ng vai tr\u00f2 nh\u01b0 ranh gi\u1edbi gi\u1eefa kh\u00f4ng gian b\u00ean trong v\u00e0 b\u00ean ngo\u00e0i c\u1ee7a h\u00ecnh c\u1ea7u. \u0110i\u1ec3m t\u00e2m c\u1ee7a h\u00ecnh c\u1ea7u (O) v\u00e0 b\u00e1n k\u00ednh (R) s\u1ebd quy\u1ebft \u0111\u1ecbnh c\u00e1c \u0111i\u1ec3m tr\u00ean m\u1eb7t c\u1ea7u, v\u1edbi m\u1ed7i \u0111i\u1ec3m n\u1eb1m c\u00e1ch \u0111i\u1ec3m t\u00e2m m\u1ed9t kho\u1ea3ng b\u1eb1ng b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u.<\/span><\/p>\n

Ngo\u00e0i ra, h\u00ecnh c\u1ea7u c\u00f3 nhi\u1ec1u t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t nh\u01b0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng qua t\u00e2m c\u1ee7a n\u00f3. M\u1ecdi \u0111\u01b0\u1eddng th\u1eb3ng qua t\u00e2m h\u00ecnh c\u1ea7u l\u00e0 tr\u1ee5c \u0111\u1ed1i x\u1ee9ng, xoay h\u00ecnh c\u1ea7u xung quanh tr\u1ee5c n\u00e0y s\u1ebd kh\u00f4ng l\u00e0m thay \u0111\u1ed5i h\u00ecnh d\u1ea1ng c\u1ee7a n\u00f3.<\/span><\/p>\n

\u00dd ngh\u0129a th\u1ef1c ti\u1ec5n c\u1ee7a di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/span><\/h2>\n

Di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u,<\/b> m\u1eb7t c\u1ea7u v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u \u0111\u1ec1u \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, t\u1eeb to\u00e1n h\u1ecdc \u0111\u1ebfn th\u1ef1c ti\u1ec5n \u1ee9ng d\u1ee5ng trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y.<\/span><\/p>\n

Di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u kh\u00f4ng ch\u1ec9 \u0111\u01a1n thu\u1ea7n l\u00e0 kh\u00e1i ni\u1ec7m to\u00e1n h\u1ecdc m\u00e0 c\u00f2n c\u00f3 \u00fd ngh\u0129a r\u1ea5t l\u1edbn trong c\u00e1c l\u0129nh v\u1ef1c k\u1ef9 thu\u1eadt v\u00e0 c\u00f4ng ngh\u1ec7. Trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t c\u1ee7a c\u00e1c v\u1eadt th\u1ec3 c\u1ea7u, ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c n\u00e0y trong l\u0129nh v\u1ef1c thi\u1ebft k\u1ebf \u0111\u1ed3 h\u1ecda, x\u00e2y d\u1ef1ng c\u00f4ng tr\u00ecnh, hay trong vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t c\u1ee7a h\u1ec7 qu\u1ea3ng c\u00e1o, thi\u1ebft k\u1ebf s\u1ea3n ph\u1ea9m. Vi\u1ec7c hi\u1ec3u v\u00e0 \u00e1p d\u1ee5ng di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u c\u0169ng \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t c\u1ee7a h\u00ecnh d\u1ea1ng tr\u00f2n trong thi\u1ebft k\u1ebf vi\u1ec5n th\u00f4ng v\u00e0 \u0111i\u1ec7n t\u1eed.<\/span><\/p>\n

\"dien-tich-hinh-cau-2\"<\/p>\n

Th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u c\u0169ng l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m kh\u00f4ng k\u00e9m ph\u1ea7n quan tr\u1ecdng. Kh\u00f4ng ch\u1ec9 trong to\u00e1n h\u1ecdc, th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u c\u00f2n \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong l\u0129nh v\u1ef1c k\u1ef9 thu\u1eadt, \u0111\u1ecba ch\u1ea5t, v\u1eadt l\u00fd, y h\u1ecdc, v\u00e0 thi\u1ebft k\u1ebf c\u00f4ng nghi\u1ec7p. V\u00ed d\u1ee5, trong c\u00f4ng nghi\u1ec7p, vi\u1ec7c t\u00ednh to\u00e1n th\u1ec3 t\u00edch c\u1ee7a c\u00e1c h\u1ed9p ch\u1ee9a, b\u1ec3 ch\u1ee9a dung d\u1ecbch hay t\u00ednh to\u00e1n th\u1ec3 t\u00edch c\u1ee7a c\u00e1c h\u00ecnh c\u1ea7u trong qu\u00e1 tr\u00ecnh thi\u1ebft k\u1ebf c\u00e1c b\u00e1nh r\u0103ng, bi v\u00e0 c\u00e1c linh ki\u1ec7n m\u00e1y m\u00f3c \u0111\u1ec1u d\u1ef1a tr\u00ean c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u. Th\u1eadm ch\u00ed, trong y h\u1ecdc, vi\u1ec7c x\u00e1c \u0111\u1ecbnh th\u1ec3 t\u00edch kh\u1ed1i u hay c\u00e1c c\u01a1 quan c\u01a1 th\u1ec3 c\u0169ng d\u1ef1a tr\u00ean nguy\u00ean l\u00fd n\u00e0y.<\/span><\/p>\n

M\u1ed1i li\u00ean k\u1ebft gi\u1eefa di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u v\u00e0 th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u<\/span><\/h2>\n

Trong h\u00ecnh h\u1ecdc, di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u l\u00e0 nh\u1eefng kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n th\u01b0\u1eddng xuy\u00ean xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u b\u00e0i to\u00e1n. C\u00e1ch t\u00ednh n\u00e0y kh\u00f4ng ch\u1ec9 \u0111\u1ee9ng \u0111\u1ed9c l\u1eadp m\u00e0 c\u00f2n k\u1ebft n\u1ed1i ch\u1eb7t ch\u1ebd v\u1edbi c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch c\u1ee7a c\u00e1c h\u00ecnh kh\u1ed1i kh\u00e1c nh\u01b0 h\u00ecnh l\u1eadp ph\u01b0\u01a1ng, h\u00ecnh tr\u1ee5 hay h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt.<\/span><\/p>\n

\"dien-tich-hinh-cau-3\"<\/p>\n

Khi ch\u00fang ta gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn th\u1ec3 t\u00edch h\u00ecnh l\u1eadp ph\u01b0\u01a1ng, h\u00ecnh tr\u1ee5, ho\u1eb7c h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, vi\u1ec7c \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c n\u00e0y c\u00f3 th\u1ec3 g\u1eb7p nhi\u1ec1u c\u00e1ch t\u00ednh di\u1ec7n t\u00edch kh\u00e1c nhau. \u0110i\u1ec1u n\u00e0y \u0111\u1eb7t ra y\u00eau c\u1ea7u c\u1ea7n k\u1ebft h\u1ee3p c\u00e1c c\u00e1ch t\u00ednh di\u1ec7n t\u00edch c\u1ee7a c\u00e1c h\u00ecnh c\u01a1 b\u1ea3n nh\u01b0 tam gi\u00e1c, h\u00ecnh vu\u00f4ng, hay h\u00ecnh ch\u1eef nh\u1eadt \u0111\u1ec3 \u0111\u01b0a ra k\u1ebft qu\u1ea3 ch\u00ednh x\u00e1c.<\/span><\/p>\n

\u0110\u1eb7c bi\u1ec7t, khi c\u00e1c d\u1ea1ng h\u00ecnh n\u00e0y k\u1ebft h\u1ee3p v\u00e0 giao nhau, vi\u1ec7c \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1ec1 di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch c\u1ee7a t\u1eebng h\u00ecnh c\u01a1 b\u1ea3n gi\u00fap x\u00e1c \u0111\u1ecbnh k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 linh ho\u1ea1t. Qua vi\u1ec7c li\u00ean k\u1ebft v\u00e0 \u00e1p d\u1ee5ng nh\u1eefng ki\u1ebfn th\u1ee9c n\u00e0y, ch\u00fang ta c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n th\u1ef1c t\u1ebf v\u00e0 ph\u1ee9c t\u1ea1p h\u01a1n trong h\u00ecnh h\u1ecdc kh\u00f4ng gian.<\/span><\/p>\n

T\u1ed5ng h\u1ee3p c\u00e1c c\u00e1ch t\u00ednh th\u1ec3 t\u00edch m\u1eb7t c\u1ea7u, di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/span><\/h2>\n

C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u l\u00e0 nh\u1eefng c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n m\u00e0 h\u1ecdc sinh th\u01b0\u1eddng c\u1ea7n h\u1ecdc thu\u1ed9c l\u00f2ng trong m\u00f4n to\u00e1n h\u00ecnh h\u1ecdc kh\u00f4ng gian. \u0110\u00e2y l\u00e0 nh\u1eefng c\u00f4ng th\u1ee9c gi\u00fap t\u00ednh to\u00e1n gi\u00fap b\u1ea1n c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u m\u1ed9t c\u00e1ch nhanh ch\u00f3ng v\u00e0 ch\u00ednh x\u00e1c.<\/span><\/p>\n

Di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u<\/span><\/h3>\n

\u0110\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/b>, b\u1ea1n c\u1ea7n ph\u1ea3i \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c sau:<\/span><\/p>\n

S = 4 x \u03c0 x r\u00b2 ho\u1eb7c S = \u03c0 x d\u00b2<\/strong><\/p>\n

Trong \u0111\u00f3: S l\u00e0 di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u, \u03c0 l\u00e0 s\u1ed1 Pi c\u00f3 gi\u00e1 tr\u1ecb kho\u1ea3ng 3.14, d l\u00e0 \u0111\u01b0\u1eddng k\u00ednh m\u1eb7t c\u1ea7u v\u00e0 r l\u00e0 b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u.\u00a0<\/span><\/p>\n

C\u00f4ng th\u1ee9c n\u00e0y d\u1ef1a tr\u00ean vi\u1ec7c di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u b\u1eb1ng 4 l\u1ea7n di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n l\u1edbn, v\u1edbi b\u00e1n k\u00ednh l\u00e0m c\u0103n c\u1ee9 ch\u00ednh. V\u00e0 \u0111\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c n\u00e0y, ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng b\u1ea5t k\u1ef3 gi\u00e1 tr\u1ecb b\u00e1n k\u00ednh ho\u1eb7c \u0111\u01b0\u1eddng k\u00ednh c\u1ee5 th\u1ec3 n\u00e0o c\u1ee7a h\u00ecnh c\u1ea7u.<\/span><\/p>\n

\"dien-tich-hinh-cau-4\"<\/p>\n

Di\u1ec7n t\u00edch xung quanh h\u00ecnh c\u1ea7u<\/span><\/h3>\n

\u0110\u1ec3 t\u00ednh di\u1ec7n t\u00edch xung quanh m\u1ed9t h\u00ecnh c\u1ea7u, ch\u00fang ta s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c\u00a0<\/span><\/p>\n

Sxq = 4\u03c0r\u00b2.\u00a0<\/strong><\/p>\n

\u0110\u00e2y l\u00e0 c\u00f4ng th\u1ee9c gi\u00fap t\u00ednh di\u1ec7n t\u00edch to\u00e0n b\u1ed9 b\u1ec1 m\u1eb7t c\u1ee7a h\u00ecnh c\u1ea7u, bao g\u1ed3m t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n c\u1ee7a n\u00f3.<\/span><\/p>\n

Theo \u0111\u00f3, di\u1ec7n t\u00edch xung quanh h\u00ecnh c\u1ea7u c\u00f3 k\u00fd hi\u1ec7u l\u00e0 Sxq, \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch nh\u00e2n b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u v\u1edbi ch\u00ednh n\u00f3 (r\u00b2), sau \u0111\u00f3 nh\u00e2n k\u1ebft qu\u1ea3 v\u1edbi 4\u03c0. \u0110i\u1ec1u n\u00e0y t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi vi\u1ec7c nh\u00e2n b\u00e1n k\u00ednh v\u1edbi 2 r\u1ed3i nh\u00e2n v\u1edbi 2\u03c0, ho\u1eb7c nh\u00e2n b\u00e1n k\u00ednh v\u1edbi ch\u00ednh n\u00f3 r\u1ed3i nh\u00e2n v\u1edbi \u03c0, t\u1eeb \u0111\u00f3 \u0111\u01b0a ra di\u1ec7n t\u00edch xung quanh h\u00ecnh c\u1ea7u.<\/span><\/p>\n

\"dien-tich-hinh-cau-5\"<\/p>\n

Th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u<\/span><\/h3>\n

Kh\u00e1c v\u1edbi <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u, <\/b>\u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i c\u1ea7u m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c, ch\u00fang ta \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c sau:<\/span><\/p>\n

V = \u2074\u2044\u2083\u03c0r\u00b3<\/strong><\/p>\n

Trong \u0111\u00f3: V ch\u00ednh th\u1ec3 t\u00edch, r ch\u00ednh l\u00e0 b\u00e1n k\u00ednh h\u00ecnh c\u1ea7u.\u00a0<\/span><\/p>\n

C\u00f4ng th\u1ee9c n\u00e0y d\u1ef1a tr\u00ean vi\u1ec7c th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i c\u1ea7u l\u00e0 ba ph\u1ea7n t\u01b0 c\u1ee7a s\u1ed1 Pi nh\u00e2n v\u1edbi l\u1eadp ph\u01b0\u01a1ng c\u1ee7a b\u00e1n k\u00ednh. V\u00e0 \u0111\u1ec3 s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c n\u00e0y, ch\u00fang ta c\u1ea7n bi\u1ebft gi\u00e1 tr\u1ecb c\u1ee7a b\u00e1n k\u00ednh ho\u1eb7c \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a h\u00ecnh c\u1ea7u. Sau \u0111\u00f3, thay gi\u00e1 tr\u1ecb n\u00e0y v\u00e0o c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh to\u00e1n th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i c\u1ea7u m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 nhanh ch\u00f3ng. V\u00e0 ngo\u00e0i ra, \u0111\u01a1n v\u1ecb c\u1ee7a th\u1ec3 t\u00edch th\u01b0\u1eddng \u0111\u01b0\u1ee3c \u0111o b\u1eb1ng \u0111\u01a1n v\u1ecb kh\u1ed1i nh\u01b0 m\u00e9t kh\u1ed1i (m\u00b3) ho\u1eb7c centimet kh\u1ed1i (cm\u00b3).<\/span><\/p>\n

\"dien-tich-hinh-cau-6\"\u00a0<\/span><\/p>\n

T\u1ed5ng h\u1ee3p m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp<\/span><\/h2>\n

Sau \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u00f3 \u0111\u00e1p \u00e1n \u0111\u1ec3 b\u1ea1n c\u00f3 th\u1ec3 v\u1eadn d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u hay th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u th\u00e0nh th\u1ea1o nh\u00e9.<\/span><\/p>\n

B\u00e0i 1<\/span><\/h3>\n

Cho m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 t\u00e2m l\u00e0 O, b\u00e1n k\u00ednh c\u1ee7a n\u00f3 l\u00e0 9m. V\u1eady <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/b> n\u00e0y l\u00e0 bao nhi\u00eau?\u00a0<\/span><\/p>\n

H\u01b0\u1edbng d\u1eabn<\/b><\/p>\n

B\u01b0\u1edbc 1: Ghi nh\u1edb c\u00f4ng th\u1ee9c<\/span><\/p>\n

H\u00e3y \u0111\u1ea3m b\u1ea3o b\u1ea1n \u0111\u00e3 ghi ch\u00e9p c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/b> v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u. Vi\u1ec7c n\u00e0y s\u1ebd gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng \u00e1p d\u1ee5ng ch\u00fang v\u00e0o b\u00e0i t\u1eadp m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c.<\/span><\/p>\n

B\u01b0\u1edbc 2: X\u00e1c \u0111\u1ecbnh b\u00e1n k\u00ednh<\/span><\/p>\n

N\u1ebfu \u0111\u1ec1 b\u00e0i cung c\u1ea5p b\u00e1n k\u00ednh th\u00ec b\u1ea1n c\u00f3 th\u1ec3 di chuy\u1ec3n ngay \u0111\u1ebfn b\u01b0\u1edbc ti\u1ebfp theo. Tuy nhi\u00ean, n\u1ebfu ch\u1ec9 c\u00f3 th\u00f4ng tin v\u1ec1 \u0111\u01b0\u1eddng k\u00ednh, h\u00e3y nh\u1edb r\u1eb1ng b\u00e1n k\u00ednh b\u1eb1ng n\u1eeda \u0111\u01b0\u1eddng k\u00ednh. V\u00ed d\u1ee5, khi \u0111\u01b0\u1eddng k\u00ednh l\u00e0 20cm, b\u00e1n k\u00ednh s\u1ebd l\u00e0 10cm.<\/span><\/p>\n

B\u01b0\u1edbc 3: \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c<\/span><\/p>\n

Sau khi \u0111\u00e3 x\u00e1c \u0111\u1ecbnh b\u00e1n k\u00ednh, h\u00e3y thay gi\u00e1 tr\u1ecb b\u00e1n k\u00ednh n\u00e0y v\u00e0o c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u S=4\u03c0R^2. B\u1eb1ng c\u00e1ch t\u00ednh to\u00e1n theo c\u00f4ng th\u1ee9c n\u00e0y, b\u1ea1n s\u1ebd thu \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 ch\u00ednh x\u00e1c cho b\u00e0i to\u00e1n.<\/span><\/p>\n

\"dien-tich-hinh-cau-7\"<\/p>\n

C\u00e1ch l\u00e0m:<\/b><\/p>\n

\u0110\u1ec3 t\u00ednh di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u khi \u0111\u00e3 bi\u1ebft \u0111\u01b0\u1ee3c b\u00e1n k\u00ednh c\u1ee7a n\u00f3, b\u1ea1n h\u00e3y s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c S = 4\u03c0R\u00b2.\u00a0<\/span><\/p>\n

V\u00e0 trong b\u00e0i to\u00e1n n\u00e0y, b\u00e1n k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u l\u00e0 9m, v\u1eady di\u1ec7n t\u00edch c\u1ee7a m\u1eb7t c\u1ea7u s\u1ebd l\u00e0:<\/span><\/p>\n

S = 4 x 3,14 x 9^2 = 1017.36 m2<\/span><\/p>\n

B\u00e0i 2<\/span><\/h3>\n

N\u1ebfu m\u1ed9t h\u00ecnh c\u1ea7u s\u1edf h\u1eefu \u0111\u01b0\u1eddng k\u00ednh d l\u00e0 4cm, th\u00ec di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u s\u1ebd l\u00e0 (cm2)<\/span><\/p>\n

A – 9\u03c0<\/span><\/p>\n

B – 36\u03c0<\/span><\/p>\n

C – 16\u03c0<\/span><\/p>\n

D – 12\u03c0<\/span><\/p>\n

\"dien-tich-hinh-cau-8\"<\/p>\n

C\u00e1ch l\u00e0m:<\/span><\/p>\n

Tr\u01b0\u1edbc h\u1ebft, v\u1edbi m\u1ed9t h\u00ecnh c\u1ea7u c\u00f3 \u0111\u01b0\u1eddng k\u00ednh d = 4, ta bi\u1ebft r\u1eb1ng b\u00e1n k\u00ednh c\u1ee7a n\u00f3 s\u1ebd l\u00e0 R = d\/2 = 2 (cm)<\/span><\/p>\n

Ti\u1ebfp theo, ta \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c: S=4\u03c0R^2. Sau khi thay gi\u00e1 tr\u1ecb v\u00e0o, ta c\u00f3<\/span><\/p>\n

S = 4\u03c0R^2 = 4\u03c02^2 = 16 \u03c0 (cm2)<\/span><\/p>\n

V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C – <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u <\/b>l\u00e0 16\u03c0 (cm2)<\/span><\/p>\n

B\u00e0i 3<\/span><\/h3>\n

Cho kh\u1ed1i c\u1ea7u c\u00f3 d = 2cm. H\u00e3y t\u00ednh th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u n\u00e0y.<\/span><\/p>\n

H\u01b0\u1edbng d\u1eabn<\/b><\/p>\n

\u0110\u1ec3 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a m\u1ed9t h\u00ecnh c\u1ea7u, b\u1ea1n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c theo tr\u00ecnh t\u1ef1 sau:<\/span><\/p>\n

B\u01b0\u1edbc 1: Vi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u ra gi\u1ea5y: V = \u2074\u2044\u2083\u03c0.r\u00b3.\u00a0<\/span><\/p>\n

B\u01b0\u1edbc 2: Khi \u0111\u1ecdc \u0111\u1ec1, n\u1ebfu cho s\u1eb5n b\u00e1n k\u00ednh th\u00ec ghi l\u1ea1i, c\u00f2n n\u1ebfu cho \u0111\u01b0\u1eddng k\u00ednh, c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c V = 1\u20446\u03c0.d\u00b3 ho\u1eb7c chia \u0111\u01b0\u1eddng k\u00ednh cho 2 \u0111\u1ec3 c\u00f3 b\u00e1n k\u00ednh r\u1ed3i \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u00e3 vi\u1ebft \u1edf b\u01b0\u1edbc tr\u01b0\u1edbc. Trong tr\u01b0\u1eddng h\u1ee3p \u0111\u1ec1 ch\u1ec9 cung c\u1ea5p di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u (S), \u0111\u1ec3 t\u00ecm b\u00e1n k\u00ednh, chia di\u1ec7n t\u00edch m\u1eb7t c\u1ea7u cho 4\u03c0 v\u00e0 l\u1ea5y c\u0103n b\u1eadc hai c\u1ee7a k\u1ebft qu\u1ea3 \u0111\u1ec3 c\u00f3 b\u00e1n k\u00ednh (r = \u221a(S\/4\u03c0)).<\/span><\/p>\n

B\u01b0\u1edbc 3: Sau khi c\u00f3 b\u00e1n k\u00ednh, ti\u1ebfn h\u00e0nh t\u00ednh l\u0169y th\u1eeba b\u1eadc 3 c\u1ee7a b\u00e1n k\u00ednh b\u1eb1ng c\u00e1ch nh\u00e2n b\u00e1n k\u00ednh v\u1edbi ch\u00ednh n\u00f3 ba l\u1ea7n.<\/span><\/p>\n

B\u01b0\u1edbc 4: thay gi\u00e1 tr\u1ecb b\u00e1n k\u00ednh l\u0169y th\u1eeba v\u00e0o c\u00f4ng th\u1ee9c V = \u2074\u2044\u2083\u03c0r\u00b3 \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u.<\/span><\/p>\n

B\u01b0\u1edbc 5: Nh\u00e2n k\u1ebft qu\u1ea3 v\u1eeba t\u00ednh \u0111\u01b0\u1ee3c v\u1edbi \u03c0 (s\u1ed1 pi) \u0111\u1ec3 ho\u00e0n thi\u1ec7n ph\u00e9p t\u00ednh v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb cu\u1ed1i c\u00f9ng c\u1ee7a th\u1ec3 t\u00edch h\u00ecnh c\u1ea7u.<\/span><\/p>\n

\"dien-tich-hinh-cau-9\"<\/p>\n

C\u00e1ch gi\u1ea3i<\/b><\/p>\n

\u0110\u1ec3 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i c\u1ea7u c\u00f3 \u0111\u01b0\u1eddng k\u00ednh d = 4 cm, ta b\u1eaft \u0111\u1ea7u b\u1eb1ng vi\u1ec7c x\u00e1c \u0111\u1ecbnh b\u00e1n k\u00ednh r c\u1ee7a h\u00ecnh c\u1ea7u. B\u00e1n k\u00ednh r \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng n\u1eeda \u0111\u01b0\u1eddng k\u00ednh, t\u1ee9c l\u00e0:<\/span><\/p>\n

r = d\/2 = 1 (cm)<\/span><\/p>\n

Ti\u1ebfp theo, \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i c\u1ea7u v\u00e0o c\u00f4ng th\u1ee9c V = \u2074\u2044\u2083\u03c0r\u00b3, ta c\u00f3:<\/span><\/p>\n

V = \u2074\u2044\u2083\u03c0r\u00b3 = 4\/3.3,14.(1)\u00b3 = 4,18 (cm\u00b3).<\/span><\/p>\n

L\u1eddi k\u1ebft<\/span><\/h2>\n

Trong b\u00e0i vi\u1ebft n\u00e0y c\u1ee7a Ho\u00e0ng H\u00e0 Mobile<\/a><\/strong>, ch\u00fang ta \u0111\u00e3 \u0111i s\u00e2u v\u00e0o vi\u1ec7c kh\u00e1m ph\u00e1 c\u00f4ng th\u1ee9c t\u00ednh <\/span>di\u1ec7n t\u00edch h\u00ecnh c\u1ea7u<\/b> v\u00e0 th\u1ec3 t\u00edch kh\u1ed1i c\u1ea7u. Vi\u1ec7c n\u1eafm v\u1eefng nh\u1eefng c\u00f4ng th\u1ee9c \u0111\u01a1n gi\u1ea3n nh\u01b0ng quan tr\u1ecdng n\u00e0y kh\u00f4ng ch\u1ec9 gi\u00fap ch\u00fang ta hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 h\u00ecnh h\u1ecdc kh\u00f4ng gian m\u00e0 c\u00f2n \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i trong th\u1ef1c t\u1ebf. Vi\u1ec7c t\u00ednh to\u00e1n di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh c\u1ea7u kh\u00f4ng ch\u1ec9 l\u00e0 ki\u1ebfn th\u1ee9c c\u1ea7n thi\u1ebft trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc \u0111\u1ec3 b\u1ea1n v\u01b0\u1ee3t qua \u0111\u01b0\u1ee3c k\u1ef3 thi m\u00e0 c\u00f2n h\u1eefu \u00edch trong c\u00e1c l\u0129nh v\u1ef1c k\u1ef9 thu\u1eadt, c\u00f4ng nghi\u1ec7p, v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c v\u00e0 c\u0169ng l\u00e0 gi\u1ea3i ph\u00e1p s\u00e1ng t\u1ea1o trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y.<\/span><\/p>\n

XEM TH\u00caM:<\/p>\n