{"id":13919,"date":"2018-03-08T22:15:31","date_gmt":"2018-03-08T22:15:31","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13919"},"modified":"2022-01-06T18:26:14","modified_gmt":"2022-01-06T18:26:14","slug":"uma-semiesfera-e-um-cilindro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13919","title":{"rendered":"Uma semiesfera e um cilindro"},"content":{"rendered":"<p><ul id='GTTabs_ul_13919' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13919' class='GTTabs_curr'><a  id=\"13919_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13919' ><a  id=\"13919_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_13919'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13920\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13920\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\" data-orig-size=\"180,245\" 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=\"S\u00f3lido\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\" class=\"alignright size-full wp-image-13920\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\" alt=\"\" width=\"180\" height=\"245\" \/><\/a>Uma semiesfera com 5 cm de raio foi colocada sobre um cilindro com 5 cm de altura e cujo raio da base mede tamb\u00e9m 5 cm, obtendo-se o s\u00f3lido geom\u00e9trico da figura.<\/p>\n<ol>\n<li>Indica, usando letras da figura.<br \/>\na) duas retas paralelas \u00e0 reta <em>OI<\/em>;<br \/>\nb) duas retas perpendiculares \u00e0 reta <em>OI<\/em>;<br \/>\nc) duas retas n\u00e3o complanares.<\/p>\n<p>Determina o volume e a \u00e1rea da superf\u00edcie do s\u00f3lido geom\u00e9trico.<\/p>\n<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13919' onClick='GTTabs_show(1,13919)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13919'>\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\/03\/9V2Pag033-18b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13920\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13920\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\" data-orig-size=\"180,245\" 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=\"S\u00f3lido\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\" class=\"alignright size-full wp-image-13920\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18b.png\" alt=\"\" width=\"180\" height=\"245\" \/><\/a><br \/>\na) Por exemplo, as retas <em>EH<\/em> e <em>BC<\/em> s\u00e3o paralelas \u00e0 reta <em>OI<\/em>;<br \/>\nb) Por exemplo, as retas <em>AB<\/em> e <em>EF<\/em> s\u00e3o perpendiculares \u00e0 reta <em>OI<\/em>;<br \/>\nc) Por exemplo, as retas <em>AB<\/em> e <em>FG<\/em> s\u00e3o n\u00e3o complanares.<br \/>\n\u00ad<\/li>\n<li>O s\u00f3lido tem\u00a0\\({\\frac{{625\\pi }}{3}}\\) cm<sup>3<\/sup> de volume:<br \/>\n\\[\\begin{array}{*{20}{l}}V&amp; = &amp;{{V_C} + {V_{SE}}}\\\\{}&amp; = &amp;{\\pi \\times {5^2} \\times 5 + \\frac{1}{2} \\times \\frac{4}{3} \\times \\pi \\times {5^3}}\\\\{}&amp; = &amp;{\\frac{5}{3} \\times \\pi \\times {5^3}}\\\\{}&amp; = &amp;{\\frac{{625\\pi }}{3}}\\end{array}\\]<br \/>\nA \u00e1rea da superf\u00edcie do s\u00f3lido \u00e9 \\({125\\pi }\\) cm<sup>2<\/sup>:<br \/>\n\\[\\begin{array}{*{20}{l}}A&amp; = &amp;{{A_{bC}} + {A_{lC}} + {A_{lSE}}}\\\\{}&amp; = &amp;{\\pi \\times {5^2} + \\left( {2\\pi \\times 5} \\right) \\times 5 + \\frac{1}{2} \\times 4 \\times \\pi \\times {5^2}}\\\\{}&amp; = &amp;{5 \\times \\pi \\times {5^2}}\\\\{}&amp; = &amp;{125\\pi }\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13919' onClick='GTTabs_show(0,13919)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Uma semiesfera com 5 cm de raio foi colocada sobre um cilindro com 5 cm de altura e cujo raio da base mede tamb\u00e9m 5 cm, obtendo-se o s\u00f3lido geom\u00e9trico da&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":13921,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,469,487,109],"series":[],"class_list":["post-13919","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-cilindro","tag-semiesfera","tag-volume"],"views":2756,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag033-18.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13919","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=13919"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13919\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13921"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13919"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}