{"id":661,"date":"2013-03-04T21:53:05","date_gmt":"2013-03-04T12:53:05","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=661"},"modified":"2021-09-14T16:04:26","modified_gmt":"2021-09-14T07:04:26","slug":"iks200701","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/iks200701\/","title":{"rendered":"\u533b\u79d1\u6b6f\u79d1\u59272007\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5e95\u9762\u306e\u534a\u5f84\u304c \\(r\\) , \u9ad8\u3055\u304c \\(h\\) \u306e\u76f4\u5186\u9310\u306e\u5074\u9762\u7a4d\u3092 \\(r\\) \u3068 \\(h\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(4\\) \u70b9 A \\(\\left( \\dfrac{\\sqrt{3}}{3} , 1 \\right)\\) , B \\(\\left( \\dfrac{\\sqrt{3}}{2} , \\dfrac{3}{2} \\right)\\) , E \\(\\left( 0 , \\dfrac{3}{2} \\right)\\) , F \\(( 0 , 1 )\\) \u3092\u8003\u3048\u308b.\r\n\u56db\u89d2\u5f62 ABEF \u3092 \\(y\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u4f53\u306e\u8868\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e\u66f2\u7dda\r\n\\[\r\nC : \\ x^2+y^2 = 3 \\quad ( 0 \\lt x \\lt \\sqrt{2} , \\ 1 \\lt y \\lt \\sqrt{3} ) \\]\r\n\u306e\u4e0a\u306e\u70b9 Q \u3092\u8003\u3048\u308b. \u70b9 Q \u3068\u540c\u3058 \\(y\\) \u5ea7\u6a19\u3092\u6301\u3064 \\(y\\) \u8ef8\u4e0a\u306e\u70b9\u3092 H \u3068\u3057, \u539f\u70b9 O \u3068\u70b9 Q \u3092\u7d50\u3076\u7dda\u5206 OQ \u304c\u76f4\u7dda \\(y = 1\\) \u3068\u4ea4\u308f\u308b\u70b9\u3092 P \u3068\u3059\u308b.\r\n\u3055\u3089\u306b\u70b9 F \\(( 0 , 1 )\\) \u3092\u3068\u308b. \u56db\u89d2\u5f62 PQHF \u3092 \\(y\\) \u8ef8\u306e\u307e\u308f\u308a\u306b \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u4f53\u306e\u9762\u306e\u3046\u3061, \u7dda\u5206 PQ \u304c \\(1\\) \u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u9762\u306e\u8868\u9762\u7a4d\u3092 \\(S\\) \u3068\u3059\u308b. \u70b9 Q \u304c\u66f2\u7dda \\(C\\) \u4e0a\u3092\u52d5\u304f\u3068\u304d \\(S\\) \u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \u5074\u9762\u306e\u6247\u5f62\u306f, \u534a\u5f84\u304c \\(\\sqrt{r^2+h^2}\\) , \u5f27\u306e\u9577\u3055\u304c \\(2 \\pi r\\) \u306a\u306e\u3067, \u5074\u9762\u7a4d\u306f\r\n\\[\r\n\\dfrac{1}{2} \\sqrt{r^2+h^2} \\cdot 2 \\pi r = \\underline{\\pi r \\sqrt{r^2+h^2}} \\ .\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    \u56de\u8ee2\u4f53\u306f\u5186\u9310\u53f0\u3068\u306a\u308b.
    \r\n\u4e0a\u9762\u306f\u8fba AF \u304c\u4f5c\u308b\u5186\u3068\u306a\u308a, \u305d\u306e\u9762\u7a4d\u306f\r\n\\[\r\n\\pi \\left( \\dfrac{\\sqrt{3}}{3} \\right)^2 = \\dfrac{\\pi}{3} \\ .\r\n\\]\r\n\u5e95\u9762\u306f\u8fba BE \u304c\u4f5c\u308b\u5186\u3068\u306a\u308a, \u305d\u306e\u9762\u7a4d\u306f\r\n\\[\r\n\\pi \\left( \\dfrac{\\sqrt{3}}{2} \\right)^2 = \\dfrac{3 \\pi}{4} \\ .\r\n\\]\r\n\u5074\u9762\u306f\u8fba OB \u304c\u4f5c\u308b\u6247\u5f62\u304b\u3089\u8fba OA \u304c\u4f5c\u308b\u6247\u5f62\u3092\u9664\u3044\u305f\u5f62\u3068\u306a\u308a, \u305d\u306e\u9762\u7a4d\u306f (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u3066\r\n\\[\\begin{align}\r\n\\pi \\cdot & \\dfrac{\\sqrt{3}}{2} \\sqrt{\\left( \\dfrac{3}{2} \\right)^2 +\\left( \\dfrac{\\sqrt{3}}{2} \\right)^2} -\\pi \\cdot \\dfrac{\\sqrt{3}}{3} \\sqrt{1^2 +\\left( \\dfrac{\\sqrt{3}}{3} \\right)^2} \\\\\r\n& =\\dfrac{3 \\pi}{2} -\\dfrac{2 \\pi}{3} \\\\\r\n& =\\dfrac{5 \\pi}{6} \\ .\r\n\\end{align}\\]\r\n\u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u9762\u7a4d\u306f\r\n\\[\r\n\\dfrac{\\pi}{3} +\\dfrac{3 \\pi}{4} +\\dfrac{5 \\pi}{6} = \\underline{\\dfrac{23 \\pi}{12}} \\ .\r\n\\]\r\n

    (3)<\/strong><\/p>\r\n

    Q \\(\\left( \\sqrt{3-t^2} , t \\right) \\ ( 1 \\lt t \\lt \\sqrt{3} )\\) \u3068\u304a\u304f\u3068, P \\(\\left( \\dfrac{\\sqrt{3-t^2}}{t} , 1 \\right)\\) \u3068\u8868\u305b\u308b.\r\n\\[\r\n\\text{OQ} = \\sqrt{3} , \\ \\text{OP} = \\dfrac{\\sqrt{3}}{t}\r\n\\]\r\n\u3068, (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\nS & = \\pi \\sqrt{3-t^2} \\cdot \\sqrt{3} -\\pi \\cdot \\dfrac{\\sqrt{3-t^2}}{t} \\cdot \\dfrac{\\sqrt{3}}{t} \\\\\r\n& = \\sqrt{3} \\pi \\cdot \\dfrac{\\left( t^2-1 \\right) \\sqrt{3-t^2}}{t^2} \\ .\r\n\\end{align}\\]\r\n\\(s = \\sqrt{3-t^2}\\) \u3068\u304a\u304f\u3068, \\(0 \\lt s \\lt \\sqrt{2} \\quad ... [1]\\) \u3067\u3042\u308a\r\n\\[\r\nS = \\sqrt{3} \\pi \\cdot \\underline{\\dfrac{\\left( 2-s^2 \\right) s}{3-s^2}} _ {[2]} \\ .\r\n\\]\r\n\u4e0b\u7dda\u90e8 [2] \u3092 \\(f(s)\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\nf'(s) & = \\dfrac{( 2-3s^2 )(3-s^2) +2s^2 (2-s^2)}{(3-s^2)^2} \\\\\r\n& = \\dfrac{s^4 -7s^2 +6}{(3-s^2)^2} \\\\\r\n& = \\dfrac{(6-s^2)(1-s^2)}{(3-s^2)^2} \\ .\r\n\\end{align}\\]\r\n[1] \u306e\u7bc4\u56f2\u3067 \\(f'(s) = 0\\) \u3092\u3068\u304f\u3068\r\n\\[\\begin{align}\r\ns^2 & = 1 , 6 \\\\\r\n\\text{\u2234} \\quad s & = 1 \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(s)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} s & (0) & \\cdots & 1 & \\cdots & ( \\sqrt{2} )\\\\ \\hline f'(s) & & + & 0 & - & \\\\ \\hline f(s) & & \\nearrow & \\text{\u6700\u5927} & \\searrow & \\end{array}\r\n\\]\r\n\u3088\u3063\u3066, \\(S\\) \u306e\u6700\u5927\u5024\u306f, \\(s = 1\\) \u3059\u306a\u308f\u3061 \\(t = \\sqrt{2}\\) \u306e\u3068\u304d\r\n\\[\r\n\\sqrt{3} \\pi \\cdot f(1) = \\underline{\\dfrac{\\sqrt{3} \\pi}{2}} \\ .\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u5404\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u5e95\u9762\u306e\u534a\u5f84\u304c \\(r\\) , \u9ad8\u3055\u304c \\(h\\) \u306e\u76f4\u5186\u9310\u306e\u5074\u9762\u7a4d\u3092 \\(r\\) \u3068 \\(h\\) \u3092\u7528\u3044\u3066\u8868\u305b. (2)\u3000\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(4\\) \u70b9 A \\(\\left( \\dfrac{ … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[93],"tags":[145,109],"class_list":["post-661","post","type-post","status-publish","format-standard","hentry","category-ikashika_2007","tag-ikashika","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/661","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=661"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/661\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}