{"id":13965,"date":"2018-03-09T18:59:17","date_gmt":"2018-03-09T18:59:17","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13965"},"modified":"2022-01-06T18:38:51","modified_gmt":"2022-01-06T18:38:51","slug":"um-reservatorio-de-gas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13965","title":{"rendered":"Um reservat\u00f3rio de g\u00e1s"},"content":{"rendered":"<p><ul id='GTTabs_ul_13965' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13965' class='GTTabs_curr'><a  id=\"13965_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13965' ><a  id=\"13965_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_13965'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13966\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13966\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png\" data-orig-size=\"520,175\" 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=\"Dep\u00f3sito de g\u00e1s\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png\" class=\"alignright wp-image-13966\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b-300x101.png\" alt=\"\" width=\"380\" height=\"128\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b-300x101.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png 520w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/a>O reservat\u00f3rio de g\u00e1s da figura, constitu\u00eddo por um cilindro e duas semiesferas, tem 3,70 m de comprimento e 90 cm de altura.<\/p>\n<ol>\n<li>Qual \u00e9 o raio das semiesferas?<\/li>\n<li>Qual \u00e9 o volume, em metros c\u00fabicos e arredondado \u00e0s d\u00e9cimas, do reservat\u00f3rio de g\u00e1s?<\/li>\n<li>O reservat\u00f3rio est\u00e1 cheio at\u00e9 tr\u00eas quartos.<br \/>\nCalcula quantos litros de g\u00e1s o reservat\u00f3rio cont\u00e9m.<\/li>\n<li>O reservat\u00f3rio vai ser pintado por fora.<br \/>\nQuantas latas de tinta de 2 litros se devem comprar, sabendo que, em m\u00e9dia, com 1 litro de tinta se pinta uma superf\u00edcie de 6 m<sup>2<\/sup>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13965' onClick='GTTabs_show(1,13965)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13965'>\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\/9V2Pag040-3b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13966\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13966\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png\" data-orig-size=\"520,175\" 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=\"Dep\u00f3sito de g\u00e1s\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png\" class=\"alignright wp-image-13966\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b-300x101.png\" alt=\"\" width=\"380\" height=\"128\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b-300x101.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3b.png 520w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/a>As semiesferas t\u00eam 45 cm de raio.<\/li>\n<li>O reservat\u00f3rio de g\u00e1s tem, aproximadamente, 2,2 m<sup>3<\/sup> de volume:<br \/>\n\\[\\begin{array}{*{20}{l}}V&amp; = &amp;{{V_{Cilindro}} + {V_{Esfera}}}\\\\{}&amp; = &amp;{\\pi \\times {{0,45}^2} \\times \\left( {3,7 &#8211; 0,9} \\right) + \\frac{4}{3}\\pi \\times {{0,45}^3}}\\\\{}&amp; = &amp;{\\pi \\times {{0,45}^2} \\times 3,4}\\\\{}&amp; = &amp;{0,6885\\pi }\\\\{}&amp; \\approx &amp;{2,2}\\end{array}\\]<\/li>\n<li>O reservat\u00f3rio cont\u00e9m, aproximadamente, 1622 litros de g\u00e1s:<br \/>\n\\[{V_{G\u00e1s}} = \\frac{3}{4} \\times 0,6885\\pi {\\;^{{m^3}}} = 1000 \\times \\frac{3}{4} \\times 0,6885\\pi {\\;^l} \\approx 1622{\\;^l}\\]<\/li>\n<li>Comecemos por determinar, em m<sup>2<\/sup>, a \u00e1rea da superf\u00edcie exterior do reservat\u00f3rio:<br \/>\n\\[A = A{}_{SE} + {A_{LateralCilindro}} = 4\\pi \\times {0,45^2} + 2\\pi \\times 0,45 \\times 2,8 = 3,33\\pi \\]<br \/>\nOra, \\(\\frac{A}{6} = \\frac{{3,33\\pi }}{6} \\approx 1,74\\).<br \/>\nLogo, prev\u00ea-se a necessidade de cerca de 1,74 litros de tinta para pintar a parte exterior do reservat\u00f3rio.<br \/>\nPortanto, deve comprar-se apenas uma lata de 2 litros de tinta.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13965' onClick='GTTabs_show(0,13965)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O reservat\u00f3rio de g\u00e1s da figura, constitu\u00eddo por um cilindro e duas semiesferas, tem 3,70 m de comprimento e 90 cm de altura. Qual \u00e9 o raio das semiesferas? Qual \u00e9&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":13967,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,108,469,482,109],"series":[],"class_list":["post-13965","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-esfera","tag-volume"],"views":1612,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag040-3.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13965","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=13965"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13965\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13967"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13965"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13965"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}