{"id":5085,"date":"2010-11-01T23:34:36","date_gmt":"2010-11-01T23:34:36","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5085"},"modified":"2022-01-19T17:12:49","modified_gmt":"2022-01-19T17:12:49","slug":"um-cone-inscrito-num-cubo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5085","title":{"rendered":"Um cone inscrito num cubo"},"content":{"rendered":"<p><ul id='GTTabs_ul_5085' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5085' class='GTTabs_curr'><a  id=\"5085_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_5085' ><a  id=\"5085_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_5085'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5086\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5086\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\" data-orig-size=\"266,283\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Cubo e cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\" class=\"alignright wp-image-5086\" title=\"Cubo e cone\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\" alt=\"\" width=\"240\" height=\"255\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg 266w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10-140x150.jpg 140w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Considera o cone inscrito num cubo com 8 cm de aresta.<\/p>\n<p>Qual o volume, arredondado \u00e0s unidades, do s\u00f3lido obtido ap\u00f3s o cubo ter sido &#8220;escavado&#8221; pelo cone?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5085' onClick='GTTabs_show(1,5085)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_5085'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"5086\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=5086\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\" data-orig-size=\"266,283\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Cubo e cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\" class=\"alignright wp-image-5086\" title=\"Cubo e cone\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg\" alt=\"\" width=\"240\" height=\"255\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10.jpg 266w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/pag119-10-140x150.jpg 140w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>O cone considerado tem 8 cm de altura e o raio da base tem comprimento 4 cm.<\/p>\n<p>Logo, o volume deste cone \u00e9 \\[{{V}_{C}}=\\frac{1}{3}\\times \\pi \\times {{4}^{2}}\\times 8=\\frac{128\\pi }{3}\\,c{{m}^{3}}\\]<\/p>\n<p>Como o volume do cubo \u00e9 ${{V}_{Cubo}}={{8}^{3}}=512\\,c{{m}^{3}}$, ent\u00e3o o volume pedido \u00e9, aproximadamente, \\[V={{V}_{Cubo}}-{{V}_{C}}=512-\\frac{128\\pi }{3}\\simeq 378\\,c{{m}^{3}}\\]<\/p>\n<p style=\"text-align: center;\">\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5085' onClick='GTTabs_show(0,5085)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera o cone inscrito num cubo com 8 cm de aresta. Qual o volume, arredondado \u00e0s unidades, do s\u00f3lido obtido ap\u00f3s o cubo ter sido &#8220;escavado&#8221; pelo cone? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20648,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,67,109],"series":[],"class_list":["post-5085","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-geometria","tag-volume"],"views":5808,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/7V2Pag119-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5085","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=5085"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5085\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20648"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5085"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}