{"id":13933,"date":"2018-03-09T00:02:14","date_gmt":"2018-03-09T00:02:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13933"},"modified":"2022-01-06T18:29:23","modified_gmt":"2022-01-06T18:29:23","slug":"um-cubo-e-uma-piramide-quadrangular-regular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13933","title":{"rendered":"Um cubo e uma pir\u00e2mide quadrangular regular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13933' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13933' class='GTTabs_curr'><a  id=\"13933_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13933' ><a  id=\"13933_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_13933'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13934\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13934\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\" data-orig-size=\"240,245\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\" class=\"alignright size-full wp-image-13934\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\" alt=\"\" width=\"240\" height=\"245\" \/><\/a>Na figura, podes ver um cubo e, a sombreado, uma pir\u00e2mide quadrangular regular.<br \/>\nA base da pir\u00e2mide coincide com a face [<em>ABCD<\/em>] do cubo.<br \/>\nO v\u00e9rtice <em>P<\/em> da pir\u00e2mide pertence \u00e0 face [<em>EFGH<\/em>] do cubo.<\/p>\n<ol>\n<li>Utilizando as letras da figura, indica uma reta que seja complanar com a reta <em>AC<\/em> e perpendicular a esta reta.<\/li>\n<li>Se a pir\u00e2mide da figura tivesse 9 cm<sup>3<\/sup> de volume, qual seria o comprimento da aresta do cubo?<br \/>\nApresenta todos os c\u00e1lculos que efetuares e, na tua resposta, indica a unidade de medida.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13933' onClick='GTTabs_show(1,13933)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13933'>\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\/2018\/03\/9V2Pag037-3b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13934\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13934\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\" data-orig-size=\"240,245\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\" class=\"alignright size-full wp-image-13934\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3b.png\" alt=\"\" width=\"240\" height=\"245\" \/><\/a>Por exemplo, a reta <em>BD<\/em> \u00e9 complanar com a reta <em>AC<\/em> e perpendicular a esta reta.<\/li>\n<li>O comprimento da aresta do cubo \u00e9 3 cm:<br \/>\n\\[\\begin{array}{*{20}{l}}{V = 9}&amp; \\Leftrightarrow &amp;{\\frac{1}{3} \\times \\overline {AB} \\times \\overline {AD} \\times \\overline {AE} = 9}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{1}{3} \\times {{\\overline {AB} }^3} = 9}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\overline {AB} }^3} = 27}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} = 3}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13933' onClick='GTTabs_show(0,13933)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, podes ver um cubo e, a sombreado, uma pir\u00e2mide quadrangular regular. A base da pir\u00e2mide coincide com a face [ABCD] do cubo. O v\u00e9rtice P da pir\u00e2mide pertence \u00e0&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":13936,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,485,471,109],"series":[],"class_list":["post-13933","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-distancias-areas-e-volumes-de-solidos","tag-9-o-ano","tag-cubo","tag-piramide","tag-volume"],"views":3495,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-3.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13933","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=13933"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13933\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13936"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13933"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13933"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13933"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13933"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}