{"id":6420,"date":"2010-12-23T02:43:50","date_gmt":"2010-12-23T02:43:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6420"},"modified":"2022-11-17T10:50:44","modified_gmt":"2022-11-17T10:50:44","slug":"cortou-se-um-cubo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6420","title":{"rendered":"Cortou-se um cubo"},"content":{"rendered":"<p><ul id='GTTabs_ul_6420' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6420' class='GTTabs_curr'><a  id=\"6420_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6420' ><a  id=\"6420_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6420'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6422\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6422\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg\" data-orig-size=\"334,334\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg\" class=\"alignright wp-image-6422\" title=\"Cubo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3-300x300.jpg\" alt=\"\" width=\"180\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3-300x300.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg 334w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>Cortou-se um cubo por um plano contendo as diagonais de duas faces paralelas.<\/p>\n<ol>\n<li>Que forma tem a sec\u00e7\u00e3o obtida?<\/li>\n<li>Sabendo que o cubo tem 4 cm de aresta, relaciona a \u00e1rea da sec\u00e7\u00e3o com a \u00e1rea de uma face.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6420' onClick='GTTabs_show(1,6420)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6420'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6422\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6422\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg\" data-orig-size=\"334,334\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg\" class=\"alignright wp-image-6422\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3-300x300.jpg\" alt=\"Cubo\" width=\"180\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3-300x300.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag-39-3.jpg 334w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>A sec\u00e7\u00e3o obtida tem a forma de um ret\u00e2ngulo.<br \/>\n\u00ad<\/li>\n<li>Esse ret\u00e2ngulo tem largura igual ao comprimento da aresta do cubo e comprimento igual \u00e0 sua diagonal facial.Determinemos o comprimento da diagonal facial do cubo: $d=\\sqrt{{{4}^{2}}+{{4}^{2}}}=\\sqrt{32}\\,cm$.\n<p>A \u00e1rea de uma face do cubo \u00e9: ${{A}_{f}}=4\\times 4=16\\,c{{m}^{2}}$.<\/p>\n<p>A \u00e1rea da sec\u00e7\u00e3o obtida \u00e9: ${{A}_{s}}=4\\times \\sqrt{32}\\simeq 22,6\\,c{{m}^{2}}$.<\/p>\n<p>Portanto, a \u00e1rea da sec\u00e7\u00e3o \u00e9 maior do que a \u00e1rea de uma face do cubo.<\/p>\n<p><strong>Nota<\/strong>: A \u00e1rea da sec\u00e7\u00e3o \u00e9 $\\sqrt{2}$ maior que a \u00e1rea de uma face: $\\frac{{{A}_{s}}}{{{A}_{f}}}=\\frac{4\\times \\sqrt{32}}{4\\times 4}=\\frac{4\\times 4\\times \\sqrt{2}}{4\\times 4}=\\sqrt{2}$, pois $\\sqrt{32}=\\sqrt{16\\times 2}=\\sqrt{16}\\times \\sqrt{2}=4\\times \\sqrt{2}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6420' onClick='GTTabs_show(0,6420)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Cortou-se um cubo por um plano contendo as diagonais de duas faces paralelas. Que forma tem a sec\u00e7\u00e3o obtida? Sabendo que o cubo tem 4 cm de aresta, relaciona a \u00e1rea&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20681,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,112],"tags":[424,67,118],"series":[],"class_list":["post-6420","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-decomposicao-de-figuras-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":3083,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/8V1Pag039-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6420"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6420\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20681"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6420"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6420"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6420"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}