{"id":13735,"date":"2018-03-03T19:14:47","date_gmt":"2018-03-03T19:14:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13735"},"modified":"2022-01-16T17:02:56","modified_gmt":"2022-01-16T17:02:56","slug":"um-cone-e-um-cubo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13735","title":{"rendered":"Um cone e um cubo"},"content":{"rendered":"<p><ul id='GTTabs_ul_13735' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13735' class='GTTabs_curr'><a  id=\"13735_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13735' ><a  id=\"13735_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_13735'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13736\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13736\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png\" data-orig-size=\"540,380\" 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=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png\" class=\"alignright size-medium wp-image-13736\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4-300x211.png\" alt=\"\" width=\"300\" height=\"211\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4-300x211.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png 540w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Considera um cone reto inscrito num cubo (a base do cone est\u00e1 inscrita na face [ABCD] do cubo e o v\u00e9rtice do cone pertence \u00e0 face [EFGH] do cubo) com 8 cm de aresta.<\/p>\n<p>Qual \u00e9, em cm<sup>3<\/sup>, o volume, arredondado \u00e0s unidades, do s\u00f3lido obtido ap\u00f3s o cone ter sido &#8220;escavado&#8221; do cubo?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13735' onClick='GTTabs_show(1,13735)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13735'>\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\/9V2Pag21-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13736\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13736\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png\" data-orig-size=\"540,380\" 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=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png\" class=\"alignright size-medium wp-image-13736\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4-300x211.png\" alt=\"\" width=\"300\" height=\"211\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4-300x211.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-4.png 540w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>\\[\\begin{array}{*{20}{l}}V&amp; = &amp;{{V_{Cubo}} &#8211; {V_{Cone}}}\\\\{}&amp; = &amp;{{8^3} &#8211; \\frac{1}{3} \\times \\pi \\times {4^2} \\times 8}\\\\{}&amp; = &amp;{512 &#8211; \\frac{{128\\pi }}{3}}\\\\{}&amp; = &amp;{\\frac{{1536 &#8211; 128\\pi }}{3}}\\\\{}&amp; \\approx &amp;{378}\\end{array}\\]<\/p>\n<p>O s\u00f3lido obtido ap\u00f3s o cone ter sido &#8220;escavado&#8221; do cubo tem, aproximadamente, 378 cm<sup>3<\/sup> de volume.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13735' onClick='GTTabs_show(0,13735)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera um cone reto inscrito num cubo (a base do cone est\u00e1 inscrita na face [ABCD] do cubo e o v\u00e9rtice do cone pertence \u00e0 face [EFGH] do cubo) com 8&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20387,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,470,109],"series":[],"class_list":["post-13735","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-volume"],"views":1268,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag021-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13735","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=13735"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13735\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20387"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13735"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}