{"id":13945,"date":"2018-03-09T01:25:36","date_gmt":"2018-03-09T01:25:36","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13945"},"modified":"2022-01-06T18:33:18","modified_gmt":"2022-01-06T18:33:18","slug":"um-prisma-e-uma-piramide-quadrangulares-regulares","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13945","title":{"rendered":"Um prisma e uma pir\u00e2mide quadrangulares regulares"},"content":{"rendered":"<p><ul id='GTTabs_ul_13945' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13945' class='GTTabs_curr'><a  id=\"13945_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13945' ><a  id=\"13945_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_13945'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13946\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13946\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\" data-orig-size=\"200,245\" 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=\"Prisma\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\" class=\"alignright size-full wp-image-13946\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\" alt=\"\" width=\"200\" height=\"245\" \/><\/a>Relativamente \u00e0 figura, sabe-se que:<\/p>\n<ul>\n<li>[<em>ABCDEFGH<\/em>] \u00e9 um prisma quadrangular regular reto;<\/li>\n<li>[<em>ABCDI<\/em>] \u00e9 uma pir\u00e2mide quadrangular regular;<\/li>\n<li>o ponto <em>I<\/em> \u00e9 o centro da face [<em>EFGH<\/em>] do prisma;<\/li>\n<li>o volume do prisma [<em>ABCDEFGH<\/em>] \u00e9 27 cm<sup>3<\/sup>.<\/li>\n<\/ul>\n<p>Sup\u00f5e agora que ao prisma [<em>ABCDEFGH<\/em>] se vai retirar a pir\u00e2mide [<em>ABCDI<\/em>].<br \/>\nQual \u00e9 o volume, em cm<sup>3<\/sup>, do s\u00f3lido que se obt\u00e9m depois de retirada a pir\u00e2mide ao prisma?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13945' onClick='GTTabs_show(1,13945)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13945'>\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\/9V2Pag039-6b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13946\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13946\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\" data-orig-size=\"200,245\" 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=\"Prisma\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\" class=\"alignright size-full wp-image-13946\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6b.png\" alt=\"\" width=\"200\" height=\"245\" \/><\/a>O s\u00f3lido que se obt\u00e9m depois de retirada a pir\u00e2mide ao prisma tem 18 cm<sup>3<\/sup> de volume:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{V_{S\u00f3lido}}}&amp; = &amp;{{V_{Prisma}} &#8211; {V_{Pir\u00e2mide}}}\\\\{}&amp; = &amp;{\\left( {\\overline {AB} \\times \\overline {AD} } \\right) \\times \\overline {AF} &#8211; \\frac{1}{3} \\times \\left( {\\overline {AB} \\times \\overline {AD} } \\right) \\times \\overline {AF} }\\\\{}&amp; = &amp;{\\frac{2}{3} \\times \\left( {\\overline {AB} \\times \\overline {AD} } \\right) \\times \\overline {AF} }\\\\{}&amp; = &amp;{\\frac{2}{3} \\times \\underbrace {\\left( {\\overline {AB} \\times \\overline {AD} } \\right) \\times \\overline {AF} }_{{V_{Prisma}}}}\\\\{}&amp; = &amp;{\\frac{2}{3} \\times 27}\\\\{}&amp; = &amp;{18}\\end{array}\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13945' onClick='GTTabs_show(0,13945)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Relativamente \u00e0 figura, sabe-se que: [ABCDEFGH] \u00e9 um prisma quadrangular regular reto; [ABCDI] \u00e9 uma pir\u00e2mide quadrangular regular; o ponto I \u00e9 o centro da face [EFGH] do prisma; o volume&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":13947,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,471,468,109],"series":[],"class_list":["post-13945","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-piramide","tag-prisma","tag-volume"],"views":2804,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-6.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13945","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=13945"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13945\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13947"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13945"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}