{"id":22915,"date":"2022-11-02T22:02:45","date_gmt":"2022-11-02T22:02:45","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=22915"},"modified":"2022-11-03T22:49:59","modified_gmt":"2022-11-03T22:49:59","slug":"comprimento-da-aresta-de-um-cubo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=22915","title":{"rendered":"Comprimento da aresta de um cubo"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_22915' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_22915' class='GTTabs_curr'><a  id=\"22915_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_22915' ><a  id=\"22915_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_22915'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Indica, para cada caso, o valor exato e o valor aproximado \u00e0s d\u00e9cimas, do comprimento da aresta de um cubo, sabendo que:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>a \u00e1rea total da superf\u00edcie do cubo \u00e9 120 cm<sup>2<\/sup>.<\/li>\n<li>o volume do cubo \u00e9 1000 cm<sup>3<\/sup>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_22915' onClick='GTTabs_show(1,22915)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_22915'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"22919\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=22919\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b.png\" data-orig-size=\"804,349\" 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_Volume-e-AreaTotal_b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b.png\" class=\"alignright wp-image-22919\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b-300x130.png\" alt=\"\" width=\"360\" height=\"156\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b-300x130.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b-768x333.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/Cubo_Volume-e-AreaTotal_b.png 804w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>Indica, para cada caso, o valor exato e o valor aproximado \u00e0s d\u00e9cimas, do comprimento da aresta de um cubo, sabendo que:<\/p>\n<\/blockquote>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>\n<blockquote>a \u00e1rea total da superf\u00edcie do cubo \u00e9 120 cm<sup>2<\/sup>.<\/blockquote>\n<\/li>\n<li>\n<blockquote>o volume do cubo \u00e9 1000 cm<sup>3<\/sup>.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>A \u00e1rea de uma face do cubo \u00e9 expressa por \\({A_f} = \\frac{{{A_T}}}{6}\\).<br \/>Logo, temos: \\({A_f} = \\frac{{120}}{6} = 20\\) cm<sup>2<\/sup>.<br \/>Assim, vem:<br \/>&#8211; Valor exato do comprimento da aresta do cubo: \\(a = \\sqrt {20} \\) cm;<br \/>&#8211; Valor aproximado \u00e0s d\u00e9cimas do comprimento da aresta do cubo: \\(a = \\sqrt {20} \\approx 4,5\\) cm.<br \/><br \/><\/li>\n<li>Como \\(a = \\sqrt[3]{V}\\), vem:<br \/>&#8211; Valor exato do comprimento da aresta do cubo: \\(a = \\sqrt[3]{{1000}} = 10\\) cm;<br \/>&#8211; Valor aproximado \u00e0s d\u00e9cimas do comprimento da aresta do cubo: \\(a = \\sqrt[3]{{1000}} = 10,0\\) cm.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_22915' onClick='GTTabs_show(0,22915)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Indica, para cada caso, o valor exato e o valor aproximado \u00e0s d\u00e9cimas, do comprimento da aresta de um cubo, sabendo que: a \u00e1rea total da superf\u00edcie do cubo \u00e9 120&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":22925,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,664],"tags":[424,266],"series":[],"class_list":["post-22915","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-numeros-reais","tag-8-o-ano","tag-numeros-reais"],"views":262,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag029-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22915","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=22915"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/22915\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/22925"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22915"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=22915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}