{"id":14256,"date":"2018-04-03T16:30:03","date_gmt":"2018-04-03T15:30:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14256"},"modified":"2022-01-11T13:46:14","modified_gmt":"2022-01-11T13:46:14","slug":"o-volume-de-um-cilindro","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14256","title":{"rendered":"O volume de um cilindro"},"content":{"rendered":"<p><ul id='GTTabs_ul_14256' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14256' class='GTTabs_curr'><a  id=\"14256_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14256' ><a  id=\"14256_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_14256'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14257\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14257\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18.png\" data-orig-size=\"280,300\" 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=\"Cilindro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18.png\" class=\"alignright wp-image-14257\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18-280x300.png\" alt=\"\" width=\"240\" height=\"257\" \/><\/a>Observa o cilindro da figura.<\/p>\n<p>Calcula o valor exato:<\/p>\n<ol>\n<li>de\u00a0\\(\\overline {KJ} \\);<\/li>\n<li>do volume do cilindro.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14256' onClick='GTTabs_show(1,14256)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14256'>\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\/04\/9V2Pag63-18.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14257\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14257\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18.png\" data-orig-size=\"280,300\" 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=\"Cilindro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18.png\" class=\"alignright wp-image-14257\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18-280x300.png\" alt=\"\" width=\"240\" height=\"257\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo [<em>IJK<\/em>], vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} J\\widehat IK = \\frac{{\\overline {KJ} }}{{\\overline {IJ} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 30^\\circ = \\frac{{\\overline {KJ} }}{{10}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{{\\sqrt 3 }}{3} = \\frac{{\\overline {KJ} }}{{10}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {KJ} = \\frac{{10\\sqrt 3 }}{3}}\\end{array}\\]<br \/>\nPortanto, \\({\\overline {KJ} = \\frac{{10\\sqrt 3 }}{3}}\\) cm.<br \/>\n\u00ad<\/li>\n<li>O cilindro tem\\(\\frac{{1000\\pi }}{3}\\) cm<sup>3<\/sup> de volume.<br \/>\n\\[V = \\pi \\times {\\left( {\\frac{{10\\sqrt 3 }}{3}} \\right)^2} \\times 10 = \\pi \\times \\frac{{100 \\times 3}}{9} \\times 10 = \\frac{{1000\\pi }}{3}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14256' onClick='GTTabs_show(0,14256)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa o cilindro da figura. Calcula o valor exato: de\u00a0\\(\\overline {KJ} \\); do volume do cilindro. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14259,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,493,490,492],"series":[],"class_list":["post-14256","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente"],"views":1742,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-18a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14256","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=14256"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14256\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14259"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14256"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}