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{"id":13792,"date":"2018-03-05T00:12:42","date_gmt":"2018-03-05T00:12:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13792"},"modified":"2022-01-16T18:38:19","modified_gmt":"2022-01-16T18:38:19","slug":"a-superficie-lateral-de-um-cone","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13792","title":{"rendered":"A superf\u00edcie lateral de um cone"},"content":{"rendered":"<p><ul id='GTTabs_ul_13792' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13792' class='GTTabs_curr'><a  id=\"13792_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13792' ><a  id=\"13792_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_13792'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina a \u00e1rea da superf\u00edcie lateral de um cone com 10 cm de geratriz e 4 cm de raio da base.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13792' onClick='GTTabs_show(1,13792)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13792'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13793\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13793\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1.png\" data-orig-size=\"844,781\" 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=\"Planifica\u00e7\u00e3o do cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1.png\" class=\"alignright size-medium wp-image-13793\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1-300x278.png\" alt=\"\" width=\"300\" height=\"278\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1-300x278.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1-768x711.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/2017-18-MF9P2-pag28-1.png 844w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>A superf\u00edcie lateral do cone \u00e9 um setor circular de raio [BV], cuja \u00e1rea \u00e9 diretamente proporcional ao comprimento do arco BAB&#8217;:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{{A_S}}}{{2\\pi \\times r}} = \\frac{{\\pi \\times {g^2}}}{{2\\pi \\times g}}}&amp; \\Leftrightarrow &amp;{\\frac{{{A_S}}}{{2\\pi \\times 4}} = \\frac{{\\pi \\times {{10}^2}}}{{2\\pi \\times 10}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{{{A_S}}}{{2\\pi \\times 4}} = 5}\\\\{}&amp; \\Leftrightarrow &amp;{{A_S} = 40\\pi }\\end{array}\\]<\/p>\n<p>Portanto, a\u00a0\u00e1rea da superf\u00edcie lateral do cone \u00e9\u00a0\\({40\\pi }\\) cm<sup>2<\/sup>.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13792' onClick='GTTabs_show(0,13792)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina a \u00e1rea da superf\u00edcie lateral de um cone com 10 cm de geratriz e 4 cm de raio da base. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20399,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,108,470],"series":[],"class_list":["post-13792","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-area","tag-cone"],"views":3264,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag028-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13792","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=13792"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13792\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20399"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13792"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13792"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13792"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13792"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}