{"id":9880,"date":"2012-10-03T09:06:57","date_gmt":"2012-10-03T08:06:57","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9880"},"modified":"2022-01-20T19:45:11","modified_gmt":"2022-01-20T19:45:11","slug":"um-copo-cilindrico-e-uma-esfera-metalica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9880","title":{"rendered":"Um copo cil\u00edndrico e uma esfera met\u00e1lica"},"content":{"rendered":"<p><ul id='GTTabs_ul_9880' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9880' class='GTTabs_curr'><a  id=\"9880_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9880' ><a  id=\"9880_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_9880'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9886\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9886\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\" data-orig-size=\"119,276\" 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;}\" data-image-title=\"Copo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\" class=\"alignright wp-image-9886\" title=\"Copo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\" alt=\"\" width=\"100\" height=\"232\" \/><\/a>Um copo cil\u00edndrico com $10$ cm de altura e $8$ cm de di\u00e2metro est\u00e1 cheio, com \u00e1gua, at\u00e9 $1$ cm do topo.<\/p>\n<p>Se uma bola met\u00e1lica com $4$ cm de di\u00e2metro for introduzida no copo, a \u00e1gua ser\u00e1 vertida?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9880' onClick='GTTabs_show(1,9880)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9880'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"9886\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9886\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\" data-orig-size=\"119,276\" 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;}\" data-image-title=\"Copo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\" class=\"alignright wp-image-9886\" title=\"Copo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/copo.jpg\" alt=\"\" width=\"100\" height=\"232\" \/><\/a>O volume da bola, em cent\u00edmetros c\u00fabicos, \u00e9:<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{{V_B}}&amp; = &amp;{\\frac{4}{3}\\pi\u00a0 \\times {2^3}}\\\\<br \/>\n{}&amp; = &amp;{\\frac{{32\\pi }}{3}}<br \/>\n\\end{array}$$<\/p>\n<p>O volume dispon\u00edvel no copo cil\u00edndrico, em cent\u00edmetros c\u00fabicos, \u00e9:<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{{V_D}}&amp; = &amp;{\\pi\u00a0 \\times {4^2} \\times 1}\\\\<br \/>\n{}&amp; = &amp;{16\\pi }<br \/>\n\\end{array}$$<\/p>\n<\/p>\n<p>A \u00e1gua n\u00e3o verte, visto que o volume da bola \u00e9 inferior ao volume dispon\u00edvel no copo cil\u00edndrico, pois ${V_B} &lt; {B_D}$.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9880' onClick='GTTabs_show(0,9880)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um copo cil\u00edndrico com $10$ cm de altura e $8$ cm de di\u00e2metro est\u00e1 cheio, com \u00e1gua, at\u00e9 $1$ cm do topo. Se uma bola met\u00e1lica com $4$ cm de di\u00e2metro&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20765,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[321,97,322],"tags":[429,430,109],"series":[],"class_list":["post-9880","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-10-o-ano","category-aplicando","category-modulo-inicial","tag-10-o-ano","tag-modulo-inicial","tag-volume"],"views":2723,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/10\/10V1Pag033-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9880","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=9880"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9880\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20765"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9880"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}