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{"id":13873,"date":"2018-03-07T11:39:08","date_gmt":"2018-03-07T11:39:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13873"},"modified":"2022-01-06T18:02:22","modified_gmt":"2022-01-06T18:02:22","slug":"a-piramide-do-louvre","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13873","title":{"rendered":"A Pir\u00e2mide do Louvre"},"content":{"rendered":"<p><ul id='GTTabs_ul_13873' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13873' class='GTTabs_curr'><a  id=\"13873_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13873' ><a  id=\"13873_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_13873'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13874\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13874\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7.png\" data-orig-size=\"520,245\" 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=\"Pir\u00e2mide do Louvre\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7.png\" class=\"alignright size-medium wp-image-13874\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7-300x141.png\" alt=\"\" width=\"300\" height=\"141\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7-300x141.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7-720x340.png 720w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7.png 520w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A Pir\u00e2mide do Louvre, inaugurada em 1988, \u00e9 regular e tem 21 m de altura.<br \/>\nA sua base \u00e9 um quadrado com 34 metros de lado.<\/p>\n<p>Determina:<\/p>\n<ol>\n<li>o volume da Pir\u00e2mide do Louvre;<\/li>\n<li>o comprimento da sua a aresta lateral (aproximado \u00e0s d\u00e9cimas).<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13873' onClick='GTTabs_show(1,13873)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13873'>\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\/02\/9V2Pag011-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13488\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13488\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" data-orig-size=\"270,220\" 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=\"Pir\u00e2mide\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" class=\"alignright size-full wp-image-13488\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-3.png\" alt=\"\" width=\"270\" height=\"220\" \/><\/a>O volume da Pir\u00e2mide do Louvre \u00e9\u00a0\\(V = \\frac{1}{3} \\times \\left( {34 \\times 34} \\right) \\times 21 = 8092\\)\u00a0 m<sup>3<\/sup>.<br \/>\n\u00ad<\/li>\n<li>O comprimento da aresta lateral (aproximado \u00e0s d\u00e9cimas) \u00e9 31,9 metros:<br \/>\n\\[\\begin{array}{*{20}{l}}{\\overline {AV} }&amp; = &amp;{\\sqrt {{{\\overline {AV&#8217;} }^2} + {{\\overline {VV&#8217;} }^2}} }\\\\{}&amp; = &amp;{\\sqrt {{{\\left( {\\frac{{34\\sqrt 2 }}{2}} \\right)}^2} + {{21}^2}} }\\\\{}&amp; = &amp;{\\sqrt {2 \\times {{17}^2} + {{21}^2}} }\\\\{}&amp; = &amp;{\\sqrt {1019} }\\\\{}&amp; \\approx &amp;{31,9}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13873' onClick='GTTabs_show(0,13873)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Pir\u00e2mide do Louvre, inaugurada em 1988, \u00e9 regular e tem 21 m de altura. A sua base \u00e9 um quadrado com 34 metros de lado. Determina: o volume da Pir\u00e2mide&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":13874,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,471,109],"series":[],"class_list":["post-13873","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-piramide","tag-volume"],"views":3998,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag031-7.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13873","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=13873"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13873\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13874"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13873"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}