{"id":6556,"date":"2011-03-01T18:08:40","date_gmt":"2011-03-01T18:08:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6556"},"modified":"2022-01-23T16:03:54","modified_gmt":"2022-01-23T16:03:54","slug":"um-balao-esferico-esta-a-ser-insuflado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6556","title":{"rendered":"Um bal\u00e3o esf\u00e9rico est\u00e1 a ser insuflado"},"content":{"rendered":"<p><ul id='GTTabs_ul_6556' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6556' class='GTTabs_curr'><a  id=\"6556_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6556' ><a  id=\"6556_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_6556'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um bal\u00e3o esf\u00e9rico est\u00e1 a ser insuflado.<\/p>\n<p>Determine a taxa de varia\u00e7\u00e3o da \u00e1rea $S$ da superf\u00edcie do bal\u00e3o em rela\u00e7\u00e3o ao raio $r$:<\/p>\n<ol>\n<li>para $r=1$;<\/li>\n<li>para $r=5$.<\/li>\n<\/ol>\n<p>Nota: A \u00e1rea da superf\u00edcie esf\u00e9rica \u00e9 dada por $A=4\\pi {{r}^{2}}$.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6556' onClick='GTTabs_show(1,6556)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6556'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, $A'(r)=(4\\pi {{r}^{2}})&#8217;=8\\pi r$.<br \/>\nLogo, $A'(1)=8\\pi $ traduz a taxa de varia\u00e7\u00e3o da \u00e1rea da superf\u00edcie do bal\u00e3o para $r=1$.<br \/>\n\u00ad<\/li>\n<li>A\u00a0taxa de varia\u00e7\u00e3o da \u00e1rea da superf\u00edcie do bal\u00e3o para $r=5$ \u00e9 $A'(5)=40\\pi $.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6556' onClick='GTTabs_show(0,6556)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um bal\u00e3o esf\u00e9rico est\u00e1 a ser insuflado. Determine a taxa de varia\u00e7\u00e3o da \u00e1rea $S$ da superf\u00edcie do bal\u00e3o em rela\u00e7\u00e3o ao raio $r$: para $r=1$; para $r=5$. Nota: A \u00e1rea&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20920,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,134],"tags":[136],"series":[],"class_list":["post-6556","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-derivadas","tag-derivada"],"views":1708,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11V2Pag194-35_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6556","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=6556"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6556\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20920"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6556"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}