{"id":13841,"date":"2018-03-06T23:10:32","date_gmt":"2018-03-06T23:10:32","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13841"},"modified":"2022-01-16T18:58:13","modified_gmt":"2022-01-16T18:58:13","slug":"uma-esfera-um-cone-e-um-cilindro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13841","title":{"rendered":"Uma esfera, um cone e um cilindro"},"content":{"rendered":"<p><ul id='GTTabs_ul_13841' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13841' class='GTTabs_curr'><a  id=\"13841_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13841' ><a  id=\"13841_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_13841'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13842\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13842\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png\" data-orig-size=\"600,284\" 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=\"Esfera, cilindro e cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png\" class=\"alignright wp-image-13842\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-300x142.png\" alt=\"\" width=\"420\" height=\"199\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-300x142.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-520x245.png 520w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-720x340.png 720w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png 600w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a>Considera a esfera, o cilindro e o cone da figura.<\/p>\n<p>Calcula:<\/p>\n<ol>\n<li>a \u00e1rea da superf\u00edcie esf\u00e9rica;<\/li>\n<li>a \u00e1rea lateral do cilindro;<\/li>\n<li>o volume de cada um dos s\u00f3lidos;<\/li>\n<li>a rela\u00e7\u00e3o entre o volume do cone e o volume do cilindro.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13841' onClick='GTTabs_show(1,13841)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13841'>\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\/9V2Pag030-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13842\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13842\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png\" data-orig-size=\"600,284\" 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=\"Esfera, cilindro e cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png\" class=\"aligncenter wp-image-13842\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-300x142.png\" alt=\"\" width=\"420\" height=\"199\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-300x142.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-520x245.png 520w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2-720x340.png 720w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2.png 600w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/a><\/p>\n<ol>\n<li>A \u00e1rea da superf\u00edcie esf\u00e9rica \u00e9 \\({A_{SE}} = 4\\pi \\times {5^2} = 100\\pi \\) cm<sup>2<\/sup>.<br \/>\n\u00ad<\/li>\n<li>A\u00a0\u00e1rea lateral do cilindro \u00e9 \\({A_{LCil}} = 2\\pi \\times 5 \\times 12 = 120\\pi \\) cm<sup>2<\/sup>.<br \/>\n\u00ad<\/li>\n<li>\\({V_E} = \\frac{4}{3}\\pi \\times {5^3} = \\frac{{500\\pi }}{3}\\) cm<sup>3<\/sup>.<br \/>\n\\({V_{Cone}} = \\frac{1}{3}\\pi \\times {5^2} \\times 12 = 100\\pi \\) cm<sup>3<\/sup>.<br \/>\n\\({V_{Cil}} = \\pi \\times {5^2} \\times 12 = 300\\pi \\) cm<sup>3<\/sup>.<br \/>\n\u00ad<\/li>\n<li>\\(\\frac{{{V_{Cone}}}}{{{V_{Cil}}}} = \\frac{{\\frac{1}{3}\\pi \\times {5^2} \\times 12}}{{\\pi \\times {5^2} \\times 12}} = \\frac{1}{3}\\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13841' onClick='GTTabs_show(0,13841)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a esfera, o cilindro e o cone da figura. Calcula: a \u00e1rea da superf\u00edcie esf\u00e9rica; a \u00e1rea lateral do cilindro; o volume de cada um dos s\u00f3lidos; a rela\u00e7\u00e3o entre&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20404,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,108,469,470,482,109],"series":[],"class_list":["post-13841","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-cilindro","tag-cone","tag-esfera","tag-volume"],"views":3680,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag030-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13841","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=13841"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13841\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20404"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13841"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13841"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13841"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}