{"id":1138,"date":"2020-06-06T17:35:05","date_gmt":"2020-06-06T15:35:05","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=1138"},"modified":"2023-06-21T16:45:34","modified_gmt":"2023-06-21T14:45:34","slug":"das-netz-des-zylinders","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=1138","title":{"rendered":"Das Netz des Zylinders"},"content":{"rendered":"\n<p>Die Auffaltung (Abrollung)  des Zylinders in die Ebene ergibt dieses Netz. Dabei ist der zentrale Bestandteil ein Rechteck (der Mantel). Dieses Rechteck hat die L\u00e4nge u<sub>AG<\/sub> , den  Umfang der Grundfl\u00e4che und die Breite (h),  die H\u00f6he des Zylinders. <br>An den parallelen L\u00e4ngen des Rechtecks sind die zwei Kreise  (Grund- und Deckfl\u00e4che)  so angeordnet, dass ihre Peripherie  das Rechteck ber\u00fchrt.<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-primary-background-color has-text-color has-background\">Diese Darstellung dient der \u00fcbersichtlichen Veranschaulichung von Oberfl\u00e4chen von K\u00f6rpern.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"355\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/06\/zylindernetz.jpg\" alt=\"\" class=\"wp-image-1140\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/06\/zylindernetz.jpg 600w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/06\/zylindernetz-300x178.jpg 300w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Abrollen des Netzes eines Zylinders\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/REXCNrmR\/width\/1366\/height\/634\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/false\/sdz\/true\/ctl\/false\" width=\"1366px\" height=\"534px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe><\/pre>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Surface Area - Unwrapping a Cylinder\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/eYQXT3EW\/width\/729\/height\/584\/border\/888888\/sfsb\/true\/smb\/false\/stb\/true\/stbh\/true\/ai\/false\/asb\/true\/sri\/true\/rc\/false\/ld\/true\/sdz\/true\/ctl\/false\" width=\"729px\" height=\"584px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Zylinder - Volumen und Oberfl\u00e4che\" width=\"860\" height=\"484\" src=\"https:\/\/www.youtube.com\/embed\/d5osGYbadFM?start=97&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"has-background\" style=\"background-color:#e9ffc6\">&#8230;weiter zur <a href=\"https:\/\/mathe-lernen.net\/?p=1143\">Berechnung  der Oberfl\u00e4che des Zylinders<\/a>.<\/p>\n\n\n\n<p><\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_1138\" class=\"pvc_stats all  \" data-element-id=\"1138\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>Die Auffaltung (Abrollung) des Zylinders in die Ebene ergibt dieses Netz. Dabei ist der zentrale Bestandteil ein Rechteck (der Mantel). Dieses Rechteck hat die L\u00e4nge uAG , den Umfang der Grundfl\u00e4che und die Breite (h), die H\u00f6he des Zylinders. An den parallelen L\u00e4ngen des Rechtecks sind die zwei Kreise (Grund- und Deckfl\u00e4che) so angeordnet, dass ihre Peripherie das Rechteck ber\u00fchrt.<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_1138\" class=\"pvc_stats all  \" data-element-id=\"1138\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959,992,1000,48],"tags":[229,293,306],"class_list":["post-1138","post","type-post","status-publish","format-standard","hentry","category-koerper","category-zylinder","category-darstellungsarten","category-kreiszylinder","tag-netz","tag-oberflaeche","tag-zylinder"],"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1138"}],"version-history":[{"count":0,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1138\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}