Độ dài của cung tròn. Diện tích hình quạt tròn và hình vành khuyên

Home Lớp 9 Toán lớp 9 - Sách Kết nối tri thức Bài 15. Độ dài của cung tròn. Diện tích hình quạt tròn và hình vành khuyênBài tập nâng cao

{"common":{"save":0,"post_id":"7936","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8356","post_id":"7936","mon_id":"1159278","chapter_id":"1159329","question":"Trên \u0111\u01b0\u1eddng tròn (O ; R) có hai \u0111i\u1ec3m A, B sao cho s\u1ed1 \u0111o cung nh\u1ecf AB b\u1eb1ng 75°. Trên (O' ; R') có hai \u0111i\u1ec3m C, D sao cho s\u1ed1 \u0111o cung nh\u1ecf CD b\u1eb1ng 45°. Bi\u1ebft hai cung nh\u1ecf AB và CD có \u0111\u1ed9 dài b\u1eb1ng nhau. T\u1ec9 s\u1ed1 di\u1ec7n tích hai hình tròn (O ; R) và (O' ; R') là:<\/p>","options":["A.<\/strong> $\\dfrac{5}{3}$<\/span>","B.<\/strong> $\\dfrac{3}{5}$<\/span>","C.<\/strong> $\\dfrac{9}{25}$<\/span>","D.<\/strong> $\\dfrac{25}{9}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"Ch\u1ecdn C.<\/strong> $\\dfrac{9}{25}$<\/span>.<\/span><\/p>T\u1eeb \u0111\u1ec1 bài ta có $\\dfrac{\\pi.R.75}{180}=\\dfrac{\\pi.R^\\prime.45}{180}$<\/span> suy ra $\\dfrac{R}{R^\\prime}=\\dfrac{45}{75}$<\/span> hay $\\dfrac{R}{R^\\prime}=\\dfrac{3}{5}$<\/span>.<\/p>T\u1ec9 s\u1ed1 di\u1ec7n tích c\u1ee7a hai hình tròn là $\u200b\\dfrac{S}{S^\\prime}=\\dfrac{\\pi.R^2}{\\pi.R^{\\prime2}}\u200b=\\bigg(\\dfrac{R}{R^\\prime}\\bigg)^2=\\dfrac{9}{25}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-05 02:02:18","option_type":"math","len":0},{"id":"8357","post_id":"7936","mon_id":"1159278","chapter_id":"1159329","question":"M\u1ed9t ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng trên m\u1ed9t \u0111\u01b0\u1eddng tròn có bán kính r = 0,4 m v\u1edbi t\u1ed1c \u0111\u1ed9 không \u0111\u1ed5i. Ch\u1ea5t \u0111i\u1ec3m chuy\u1ec3n \u0111\u1ed9ng h\u1ebft m\u1ed9t vòng quanh \u0111\u01b0\u1eddng tròn \u0111ó trong 20 s. T\u1ed1c \u0111\u1ed9 c\u1ee7a ch\u1ea5t \u0111i\u1ec3m (theo \u0111\u01a1n v\u1ecb m\/s và làm tròn k\u1ebft qu\u1ea3 \u0111\u1ebfn hàng ph\u1ea7n ch\u1ee5c) là:<\/p>","options":["A.<\/strong> 0,4 m\/s","B.<\/strong> 0,3 m\/s","C.<\/strong> 0,2 m\/s","D.<\/strong> 0,1 m\/s"],"correct":"4","level":"3","hint":"","answer":"Ch\u1ecdn D.<\/strong> 0,1 m\/s.<\/span><\/p>Chu vi c\u1ee7a \u0111\u01b0\u1eddng tròn là $C=2\\pi.r=2\\pi.0,4=0,8\\pi$<\/span> (m).<\/p>V\u1eady t\u1ed1c \u0111\u1ed9 c\u1ee7a ch\u1ea5t \u0111i\u1ec3m là $v=\\dfrac{0,8\\pi}{20}\\approx0,1$<\/span> (m\/s).<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-05 02:06:40","option_type":"txt","len":0},{"id":"8360","post_id":"7936","mon_id":"1159278","chapter_id":"1159329","question":"M\u1ed9t con l\u1eafc treo th\u1eb3ng \u0111\u1ee9ng di chuy\u1ec3n t\u1eeb v\u1ecb trí A \u0111\u1ebfn v\u1ecb trí B. Bi\u1ebft s\u1ee3i dây OA có \u0111\u1ed9 dài b\u1eb1ng $l$<\/span> và tia OA t\u1ea1o v\u1edbi ph\u01b0\u01a1ng th\u1eb3ng \u0111\u1ee9ng góc 2α. \u0110\u1ed9 dài quãng \u0111\u01b0\u1eddng AB mà con l\u1eafc \u0111ó \u0111ã di chuy\u1ec3n là:<\/p><svg height=\"170\" width=\"185\"> <g><title><\/title><rect fill=\"#ffffff\" height=\"172\" id=\"canvas_background\" width=\"187\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_3\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><g id=\"svg_9\"> <ellipse cx=\"91.72159\" cy=\"21.53901\" fill=\"#fff\" id=\"svg_1\" rx=\"122.12793\" ry=\"138.59993\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"92.94287\" cy=\"22.925\" fill=\"#000000\" id=\"svg_2\" rx=\"2.44256\" ry=\"2.772\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_4\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"92.33223\" x2=\"21.49804\" y1=\"22.23201\" y2=\"135.88395\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"94.77479\" x2=\"164.38771\" y1=\"22.23201\" y2=\"133.11195\"><\/line> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"116\" id=\"svg_6\" stroke=\"#ffffff\" stroke-width=\"9.5\" transform=\"matrix(0.6829306973031666,1.1490455134220494,-1.0124863960208637,0.7750409850427511,128.86151301062927,-200.78765068330978) \" width=\"203\" x=\"76.30291\" y=\"-10.60379\"><\/rect> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"223.14589\" id=\"svg_7\" stroke=\"#ffffff\" stroke-width=\"9.5\" width=\"65.94908\" x=\"-50\" y=\"-40.13796\"><\/rect> <\/g> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_10\" stroke=\"#000000\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" x1=\"92.5\" x2=\"93\" y1=\"25.25\" y2=\"158.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" transform=\"rotate(-68 78.5,62.75) \" x=\"74.5\" xml:space=\"preserve\" y=\"71.25\">(<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000000\" stroke-width=\"0\" text-anchor=\"start\" x=\"60.5\" xml:space=\"preserve\" y=\"89.25\">2<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Courier New’, Courier, monospace\" font-size=\"24\" id=\"svg_17\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"72.5\" xml:space=\"preserve\" y=\"88.25\">a<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Courier New’, Courier, monospace\" font-size=\"24\" font-weight=\"bold\" id=\"svg_19\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"84.5\" xml:space=\"preserve\" y=\"15.25\">O<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Courier New’, Courier, monospace\" font-size=\"24\" font-weight=\"bold\" id=\"svg_20\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.5\" xml:space=\"preserve\" y=\"146.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Courier New’, Courier, monospace\" font-size=\"24\" font-weight=\"bold\" id=\"svg_21\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"166.5\" xml:space=\"preserve\" y=\"144.25\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Trebuchet MS’, Gadget, sans-serif\" font-size=\"24\" id=\"svg_22\" stroke=\"#000000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"33.5\" xml:space=\"preserve\" y=\"87.25\">l<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> $\\dfrac{\\pi.l.\\alpha}{180}$<\/span>","B.<\/strong> $\\dfrac{\\pi.l.\\alpha}{45}$<\/span>","C.<\/strong> $\\dfrac{\\pi.l.\\alpha}{90}$<\/span>","D.<\/strong> $\\dfrac{\\pi.l.\\alpha}{360}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"Ch\u1ecdn B.<\/strong> $\\dfrac{\\pi.l.\\alpha}{45}$<\/span>.<\/span><\/p>Góc \u0111\u01b0\u1ee3c t\u1ea1o thành khi con l\u1eafc di chuy\u1ec3n t\u1eeb v\u1ecb trí A \u0111\u1ebfn v\u1ecb trí B là 4α.<\/p>Khi \u0111ó \u0111\u1ed9 dài quãng \u0111\u01b0\u1eddng con l\u1eafc \u0111i \u0111\u01b0\u1ee3c là $\\dfrac{\\pi.R.n}{180}=\\dfrac{\\pi.l.4\\alpha}{180}=\\dfrac{\\pi.l.\\alpha}{45}$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-05 02:24:52","option_type":"math","len":0}]}