{"id":13939,"date":"2018-03-09T00:39:22","date_gmt":"2018-03-09T00:39:22","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13939"},"modified":"2022-01-16T19:25:33","modified_gmt":"2022-01-16T19:25:33","slug":"um-vulcao-de-agua-da-alameda-dos-oceanos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13939","title":{"rendered":"Um <i>vulc\u00e3o de \u00e1gua<\/i> da Alameda dos Oceanos"},"content":{"rendered":"<p><ul id='GTTabs_ul_13939' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13939' class='GTTabs_curr'><a  id=\"13939_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13939' ><a  id=\"13939_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_13939'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13941\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13941\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png\" data-orig-size=\"710,390\" 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=\"Vulc\u00e3o de \u00e1gua\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png\" class=\"alignright wp-image-13941\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b-300x165.png\" alt=\"\" width=\"480\" height=\"264\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b-300x165.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png 710w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a>Na fotografia, podes observar um dos <em>vulc\u00f5es de \u00e1gua<\/em> da Alameda dos Oceanos, no Parque das Na\u00e7\u00f5es, em Lisboa. Estes <em>vulc\u00f5es<\/em> expelem, periodicamente, jatos de \u00e1gua.<br \/>\nNa figura, est\u00e1 representado um cone. A parte sombreada desta figura \u00e9 um esquema do s\u00f3lido que serviu de base \u00e0 constru\u00e7\u00e3o do <em>vulc\u00e3o de \u00e1gua<\/em>.<\/p>\n<p>As medidas de comprimento indicadas est\u00e3o expressas em metros.<br \/>\n1,8 m e 0,6 m s\u00e3o os comprimentos dos raios das duas circunfer\u00eancias.<br \/>\nA altura do cone \u00e9 6 m.<\/p>\n<p>Determina, em metros c\u00fabicos, o volume do s\u00f3lido representado no esquema a sombreado.<br \/>\nIndica o resultado arredondado \u00e0s unidades e apresenta todos os c\u00e1lculos que efetuares.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13939' onClick='GTTabs_show(1,13939)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13939'>\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\/9V2Pag037-4b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13941\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13941\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png\" data-orig-size=\"710,390\" 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=\"Vulc\u00e3o de \u00e1gua\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png\" class=\"wp-image-13941 aligncenter\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b-300x165.png\" alt=\"\" width=\"480\" height=\"264\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b-300x165.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4b.png 710w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a>O s\u00f3lido representado no esquema a sombreado tem, aproximadamente, 20 m<sup>3<\/sup>\u00a0de volume:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{V_{S\u00f3lido Sombreado}}}&amp; = &amp;{{V_{Cone Grande}} &#8211; {V_{Cone Pequeno}}}\\\\{}&amp; = &amp;{\\frac{1}{3} \\times \\pi \\times {{1,8}^2} \\times 6 &#8211; \\frac{1}{3} \\times \\pi \\times {{0,6}^2} \\times 2}\\\\{}&amp; = &amp;{\\frac{\\pi }{3} \\times \\left( {{{1,8}^2} \\times 6 &#8211; {{0,6}^2} \\times 2} \\right)}\\\\{}&amp; = &amp;{\\frac{\\pi }{3} \\times 18,72}\\\\{}&amp; = &amp;{6,24 \\times \\pi }\\\\{}&amp; \\approx &amp;{20}\\end{array}\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13939' onClick='GTTabs_show(0,13939)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na fotografia, podes observar um dos vulc\u00f5es de \u00e1gua da Alameda dos Oceanos, no Parque das Na\u00e7\u00f5es, em Lisboa. Estes vulc\u00f5es expelem, periodicamente, jatos de \u00e1gua. Na figura, est\u00e1 representado um&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20408,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,470,488,109],"series":[],"class_list":["post-13939","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-cone","tag-tronco-de-cone","tag-volume"],"views":3878,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag037-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13939","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=13939"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13939\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20408"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13939"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}