{"id":13181,"date":"2018-01-08T22:09:23","date_gmt":"2018-01-08T22:09:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13181"},"modified":"2022-01-16T22:17:22","modified_gmt":"2022-01-16T22:17:22","slug":"area-de-um-setor-circular-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13181","title":{"rendered":"\u00c1rea de um setor circular"},"content":{"rendered":"<p><ul id='GTTabs_ul_13181' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13181' class='GTTabs_curr'><a  id=\"13181_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13181' ><a  id=\"13181_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_13181'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/setor.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13182\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13182\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/setor.png\" data-orig-size=\"245,225\" 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\/01\/setor.png\" class=\"alignright size-full wp-image-13182\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/setor.png\" alt=\"\" width=\"245\" height=\"225\" \/><\/a>Na figura observas um c\u00edrculo com 5 cm de raio, onde foi pintado a azul o setor circular determinado pelo \u00e2ngulo ao centro AOB, com 30\u00ba de amplitude.<\/p>\n<ol>\n<li>Qual \u00e9 a \u00e1rea e o per\u00edmetro do c\u00edrculo representado na figura?<br \/>\nApresenta os c\u00e1lculos efetuados.<\/li>\n<li>Que parte da \u00e1rea do c\u00edrculo representa a \u00e1rea do setor circular sombreado?<br \/>\nE que parte do per\u00edmetro do c\u00edrculo representa o comprimento do arco a vermelho, resultante da interse\u00e7\u00e3o da circunfer\u00eancia com o \u00e2ngulo ao centro?<\/li>\n<li>Qual \u00e9 a \u00e1rea do setor circular?<br \/>\nApresenta os c\u00e1lculos efetuados.<\/li>\n<li>Determina o comprimento do arco AB.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13181' onClick='GTTabs_show(1,13181)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13181'>\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\/01\/setor.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13182\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13182\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/setor.png\" data-orig-size=\"245,225\" 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\/01\/setor.png\" class=\"alignright size-full wp-image-13182\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/setor.png\" alt=\"\" width=\"245\" height=\"225\" \/><\/a>A \u00e1rea (em cm<sup>2<\/sup>) e o per\u00edmetro (em cm) do c\u00edrculo representado na figura s\u00e3o, respetivamente:<br \/>\n\\[\\begin{array}{*{20}{c}}{{A_\\bigcirc } = \\pi \\times {5^2} = 25\\pi }&amp;{}&amp;{}&amp;{{P_\\bigcirc } = 2\\pi \\times 5 = 10\\pi }\\end{array}\\]<br \/>\n\u00ad<\/li>\n<li>A \u00e1rea do setor circular sombreado \u00e9 \\(\\frac{{30^\\circ }}{{360^\\circ }} = \\frac{1}{{12}}\\) da \u00e1rea do c\u00edrculo.<br \/>\nO comprimento do arco a vermelho \u00e9 \\(\\frac{{30^\\circ }}{{360^\\circ }} = \\frac{1}{{12}}\\) do per\u00edmetro do c\u00edrculo.<br \/>\n\u00ad<\/li>\n<li>O setor circular tem \\[{A_{Setor}} = \\frac{1}{{12}} \\times {A_\\bigcirc } = \\frac{1}{{12}}\\pi \\times {5^2} = \\frac{{25\\pi }}{{12}}\\] cm<sup>2<\/sup> de \u00e1rea.<br \/>\n\u00ad<\/li>\n<li>O arco AB tem \\[l = \\frac{1}{{12}} \\times {P_\\bigcirc } = \\frac{1}{{12}} \\times 2\\pi \\times 5 = \\frac{{5\\pi }}{6}\\] cm de comprimento.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13181' onClick='GTTabs_show(0,13181)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura observas um c\u00edrculo com 5 cm de raio, onde foi pintado a azul o setor circular determinado pelo \u00e2ngulo ao centro AOB, com 30\u00ba de amplitude. Qual \u00e9 a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20429,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,278],"tags":[426,457,284],"series":[],"class_list":["post-13181","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-setor-circular"],"views":9764,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/01\/9V1Pag116-T5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13181","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=13181"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13181\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20429"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13181"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}