Hình trụ và hình nón - Bài tập trung bình

Home Lớp 9 Toán lớp 9 - Sách Kết nối tri thức Bài 31. Hình trụ và hình nónBài tập trung bình

{"common":{"save":0,"post_id":"7991","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"10681","post_id":"7991","mon_id":"1159278","chapter_id":"1159334","question":"Cho hình tr\u1ee5 có bán kính \u0111áy 5 cm, chi\u1ec1u cao 4 cm. Di\u1ec7n tích toàn ph\u1ea7n c\u1ee7a hình tr\u1ee5 này là<\/p>","options":["A.<\/strong> $90\\pi\\;(cm^2)$<\/span>.","B.<\/strong> $96\\pi\\;(cm^2)$<\/span>.","C.<\/strong> $94\\pi\\;(cm^2)$<\/span>.","D.<\/strong> $96\\pi\\;(cm^2)$<\/span>."],"correct":"1","level":"2","hint":"","answer":"Ch\u1ecdn A.<\/strong> $90\\pi\\;(cm^2)$<\/span>.<\/span><\/p>Theo bài ra ta có r = 5 cm , h = 4 cm.<\/p>Di\u1ec7n tích toàn ph\u1ea7n c\u1ee7a hình tr\u1ee5 là:<\/p>$S_{tp}=S_{xq}+2.S_\u0111=2\\pi rh+2\\pi r^2=2\\pi.5.4+2\\pi.5^2=90\\pi\\;(cm^2)$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-04-01 08:55:19","option_type":"math","len":0},{"id":"10683","post_id":"7991","mon_id":"1159278","chapter_id":"1159334","question":"Cho hình ch\u1eef nh\u1eadt MNPQ có MN = 16 cm, NP = 12 cm. Khi quay hình ch\u1eef nh\u1eadt \u0111ã cho m\u1ed9t vòng quanh c\u1ea1nh MN ta \u0111\u01b0\u1ee3c m\u1ed9t hình tr\u1ee5 có di\u1ec7n tích toàn ph\u1ea7n b\u1eb1ng (l\u1ea5y π = 3,14):<\/p>","options":["A.<\/strong> 1659 (cm²).","B.<\/strong> 2659,18 (cm²).","C.<\/strong> 2110,08 (cm²).","D.<\/strong> 1660 (cm²)."],"correct":"3","level":"2","hint":"","answer":"Ch\u1ecdn C.<\/strong> 2110,08 (cm²).<\/span><\/p>Ta có hình v\u1ebd:<\/p><svg height=\"280\" width=\"180\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"282\" id=\"canvas_background\" width=\"182\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_19\"> <path d=\"m173.1014,68.98709c0,17.85721 -37.60809,32.33334 -84.00002,32.33334m84.00002,-32.33334l0,0c0,17.85721 -37.60809,32.33334 -84.00002,32.33334c-46.39191,0 -83.99999,-14.4761 -83.99999,-32.33334m0,0l0,0c0,-17.85719 37.60808,-32.33333 83.99999,-32.33333c46.39193,0 84.00002,14.47614 84.00002,32.33333l0,129.3334c0,17.85719 -37.60809,32.33328 -84.00002,32.33328c-46.39191,0 -83.99999,-14.47609 -83.99999,-32.33328l0,-129.3334z\" fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"3\"><\/path> <ellipse cx=\"89.27778\" cy=\"201.08334\" fill=\"none\" id=\"svg_2\" rx=\"84\" ry=\"28.5\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-opacity=\"null\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_7\" stroke=\"#ffffff\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"2\" x1=\"89.27778\" x2=\"89.27778\" y1=\"65.58333\" y2=\"221.58333\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"89.27778\" x2=\"89.27778\" y1=\"4.58333\" y2=\"272.58333\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" transform=\"rotate(24.896100997924805 117.27777099609376,80.29166412353516) \" x1=\"87.21825\" x2=\"147.3373\" y1=\"80.2605\" y2=\"80.32283\"><\/line> <ellipse cx=\"143.27778\" cy=\"93.58333\" fill=\"#000000\" id=\"svg_6\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"2\"><\/ellipse> <ellipse cx=\"89.77778\" cy=\"67.58333\" fill=\"#000000\" id=\"svg_5\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"3\"><\/ellipse> <line fill=\"none\" id=\"svg_8\" stroke=\"#000000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"2\" x1=\"143.27778\" x2=\"143.27778\" y1=\"95.58334\" y2=\"220.58333\"><\/line> <line fill=\"none\" id=\"svg_9\" stroke=\"#ffffff\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"3\" x1=\"89.27778\" x2=\"89.27778\" y1=\"81.58333\" y2=\"222.58333\"><\/line> <ellipse cx=\"143.27778\" cy=\"222.58333\" fill=\"#000000\" id=\"svg_10\" rx=\"3\" ry=\"3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"2\"><\/ellipse> <ellipse cx=\"89.27778\" cy=\"198.58333\" fill=\"#000000\" id=\"svg_11\" rx=\"2\" ry=\"2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"2\"><\/ellipse> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_12\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" transform=\"rotate(24.896100997924805 117.27777099609376,211.29165649414062) \" x1=\"87.21825\" x2=\"147.3373\" y1=\"211.2605\" y2=\"211.32283\"><\/line> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"61.27778\" xml:space=\"preserve\" y=\"71.58333\">M<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"64.27778\" xml:space=\"preserve\" y=\"204.58333\">N<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_15\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"144.27778\" xml:space=\"preserve\" y=\"246.58333\">P<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_16\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"144.27778\" xml:space=\"preserve\" y=\"112.58333\">Q<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_17\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"37.27778\" xml:space=\"preserve\" y=\"152.58333\">16 cm<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"17\" id=\"svg_18\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(25 116.42361450195311,199.80555725097653) \" x=\"93.27778\" xml:space=\"preserve\" y=\"205.58333\">12 cm<\/text> <\/g> <\/g> <\/svg><\/span><\/p>Hình tr\u1ee5 sinh ra có chi\u1ec1u cao h = MN = 16 cm ; bán kính \u0111áy r = NP = 12 cm.<\/p>Di\u1ec7n tích toàn ph\u1ea7n c\u1ee7a hình tr\u1ee5 trên là:<\/p>$S_{tp}=S_{xq}+2.S_\u0111=2\\pi rh+2\\pi r^2$<\/span><\/p>      $=2\\pi.12.16+2\\pi.12^2=672\\pi\\\\=672.3,14=2110,08\\;(cm^2)$<\/span><\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-04-01 09:07:20","option_type":"txt","len":2},{"id":"10684","post_id":"7991","mon_id":"1159278","chapter_id":"1159334","question":"N\u1ebfu t\u0103ng bán kính \u0111áy c\u1ee7a hình tr\u1ee5 lên 4 l\u1ea7n và gi\u1eef nguyên chi\u1ec1u cao thì th\u1ec3 tích m\u1edbi c\u1ee7a hình tr\u1ee5<\/p>","options":["A.<\/strong> g\u1ea5p 4 l\u1ea7n th\u1ec3 tích c\u0169.","B.<\/strong> g\u1ea5p 8 l\u1ea7n th\u1ec3 tích c\u0169.","C.<\/strong> g\u1ea5p 12 l\u1ea7n th\u1ec3 tích c\u0169.","D.<\/strong> g\u1ea5p 16 l\u1ea7n th\u1ec3 tích c\u0169."],"correct":"4","level":"2","hint":"","answer":"Ch\u1ecdn D.<\/strong> g\u1ea5p 16 l\u1ea7n th\u1ec3 tích c\u0169.<\/span><\/p>Th\u1ec3 tích ban \u0111\u1ea7u c\u1ee7a hình tr\u1ee5 là: $V_1=\\pi r^2h$<\/span>.<\/p>Bán kính t\u0103ng lên 4 l\u1ea7n nên bán kính m\u1edbi là R = 4r.<\/p>Khi \u0111ó th\u1ec3 tích m\u1edbi c\u1ee7a hình tr\u1ee5 là $V_2=\\pi R^2h=\\pi.(4r)^2.h=16\\pi r^2h=16V_1$<\/span>.<\/p>V\u1eady th\u1ec3 tích m\u1edbi g\u1ea5p 16 l\u1ea7n th\u1ec3 tích ban \u0111\u1ea7u.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2025-04-01 09:14:54","option_type":"txt","len":2}]}