{"id":13412,"date":"2018-02-01T08:25:51","date_gmt":"2018-02-01T08:25:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13412"},"modified":"2022-01-17T15:00:04","modified_gmt":"2022-01-17T15:00:04","slug":"um-setor-circular","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13412","title":{"rendered":"Um setor circular&#8230;"},"content":{"rendered":"<p><ul id='GTTabs_ul_13412' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13412' class='GTTabs_curr'><a  id=\"13412_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13412' ><a  id=\"13412_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_13412'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13413\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13413\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4.png\" data-orig-size=\"305,215\" 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\/9V1Pag144-4.png\" class=\"alignright size-medium wp-image-13413\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4-300x211.png\" alt=\"\" width=\"300\" height=\"211\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4-300x211.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4.png 305w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considera a figura ao lado.<\/p>\n<ol>\n<li>Qual \u00e9 o trajeto mais longo: o vermelho ou o azul? Justifica.<\/li>\n<li>Compara as \u00e1reas cor de laranja e amarela.<br \/>\nApresenta todos os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13412' onClick='GTTabs_show(1,13412)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13412'>\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\/9V1Pag144-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13413\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13413\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4.png\" data-orig-size=\"305,215\" 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\/9V1Pag144-4.png\" class=\"alignright size-medium wp-image-13413\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4-300x211.png\" alt=\"\" width=\"300\" height=\"211\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4-300x211.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4.png 305w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Em cent\u00edmetros, os comprimentos dos trajetos s\u00e3o os seguintes:<br \/>\n\\[\\begin{array}{*{20}{l}}{{T_{Azul}} = \\frac{{120^\\circ }}{{360^\\circ }} \\times 2 \\times \\pi \\times 3 = 2\\pi \\approx 6,28}\\\\{{T_{Vermelho}} = \\frac{{120^\\circ }}{{360^\\circ }} \\times 2 \\times \\pi \\times 2 + 2 = \\frac{{4\\pi }}{3} + 2 = \\frac{{4\\pi + 6}}{3} \\approx 6,19}\\end{array}\\]<br \/>\nPortanto, o trajeto azul \u00e9 mais longo.<br \/>\n\u00ad<\/li>\n<li>Em cent\u00edmetros quadrados, as \u00e1reas das cores consideradas s\u00e3o as seguintes:<br \/>\n\\[\\begin{array}{*{20}{l}}{{A_{Amarela}} = \\frac{{120^\\circ }}{{360^\\circ }} \\times \\pi \\times {2^2} = \\frac{{4\\pi }}{3}}\\\\{{A_{Laranja}} = \\frac{{120^\\circ }}{{360^\\circ }} \\times \\pi \\times {3^2} &#8211; {A_{Amarela}} = \\frac{{120^\\circ }}{{360^\\circ }} \\times \\pi \\times \\left( {{3^2} &#8211; {2^2}} \\right) = \\frac{{5\\pi }}{3}}\\end{array}\\]<br \/>\nPortanto, a \u00e1rea cor de laranja \u00e9 superior \u00e0 \u00e1rea amarela.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13412' onClick='GTTabs_show(0,13412)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a figura ao lado. Qual \u00e9 o trajeto mais longo: o vermelho ou o azul? Justifica. Compara as \u00e1reas cor de laranja e amarela. Apresenta todos os c\u00e1lculos que efetuares.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20491,"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-13412","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":1928,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V1Pag144-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13412","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=13412"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13412\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20491"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13412"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}