{"id":13416,"date":"2018-02-01T08:58:22","date_gmt":"2018-02-01T08:58:22","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13416"},"modified":"2022-01-17T15:03:50","modified_gmt":"2022-01-17T15:03:50","slug":"a-area-de-um-setor-circular-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13416","title":{"rendered":"A \u00e1rea de um setor circular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13416' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13416' class='GTTabs_curr'><a  id=\"13416_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13416' ><a  id=\"13416_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_13416'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina a \u00e1rea de um setor circular, sabendo que o arco que lhe corresponde mede \\(22\\pi \\) cm e que a circunfer\u00eancia tem 40 cm de raio.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13416' onClick='GTTabs_show(1,13416)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13416'>\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\/02\/360px-Circle_arc.svg.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13418\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13418\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/360px-Circle_arc.svg.png\" data-orig-size=\"360,320\" 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=\"Setor circular\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/360px-Circle_arc.svg.png\" class=\"alignright size-medium wp-image-13418\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/360px-Circle_arc.svg-300x267.png\" alt=\"\" width=\"300\" height=\"267\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/360px-Circle_arc.svg-300x267.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/360px-Circle_arc.svg.png 360w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>As \u00e1reas dos setores circulares e os comprimentos dos arcos s\u00e3o diretamente proporcionais, logo tem-se:<\/p>\n<p>\\[\\frac{{{A_\\bigcirc }}}{{{P_\\bigcirc }}} = \\frac{{{A_{Setor}}}}{{{C_{Arco{\\rm{ }}do{\\rm{ }}Setor}}}}\\]<\/p>\n<p>Substituindo os valores conhecidos na express\u00e3o anterior, vem (em cent\u00edmetros quadrados):<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{\\pi \\times {{40}^2}}}{{2\\pi \\times 40}} = \\frac{{{A_{Setor}}}}{{22\\pi }}}&amp; \\Leftrightarrow &amp;{{A_{Setor}} = \\frac{{\\pi \\times {{40}^2} \\times 22\\pi }}{{2\\pi \\times 40}}}\\\\{}&amp; \\Leftrightarrow &amp;{{A_{Setor}} = \\pi \\times 40 \\times 11}\\\\{}&amp; \\Leftrightarrow &amp;{{A_{Setor}} = 440\\pi }\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13416' onClick='GTTabs_show(0,13416)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina a \u00e1rea de um setor circular, sabendo que o arco que lhe corresponde mede \\(22\\pi \\) cm e que a circunfer\u00eancia tem 40 cm de raio. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20492,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,457,188,284],"series":[],"class_list":["post-13416","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-circunferencia-e-poligonos","tag-9-o-ano","tag-arco-de-circunferencia","tag-circunferencia","tag-setor-circular"],"views":2686,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13416","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=13416"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13416\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20492"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13416"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13416"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13416"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}