{"id":13949,"date":"2018-03-09T01:56:58","date_gmt":"2018-03-09T01:56:58","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13949"},"modified":"2022-01-16T19:30:09","modified_gmt":"2022-01-16T19:30:09","slug":"uma-barraca-de-praia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13949","title":{"rendered":"Uma barraca de praia"},"content":{"rendered":"<p><ul id='GTTabs_ul_13949' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13949' class='GTTabs_curr'><a  id=\"13949_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13949' ><a  id=\"13949_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_13949'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13951\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13951\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png\" data-orig-size=\"1005,402\" 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=\"Barraca de praia\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png\" class=\"alignright wp-image-13951\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b-300x120.png\" alt=\"\" width=\"480\" height=\"192\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b-300x120.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b-768x307.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png 1005w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a>Na praia do parque de campismo existem barracas como as indicadas na fotografia.<br \/>\nAo lado da fotografia est\u00e1 um esquema da estrutura de uma dessas barracas.<\/p>\n<p>Relativamente \u00e0 figura, sabe-se:<\/p>\n<ul>\n<li>[ABCDEFGH] \u00e9 um prisma quadrangular regular;<\/li>\n<li>[EFGHI] \u00e9 uma pir\u00e2mide quadrangular regular;<\/li>\n<li>[IK] \u00e9 a altura da pir\u00e2mide [EFGHI];<\/li>\n<li>[IJ] \u00e9 uma altura do tri\u00e2ngulo [RFI].<\/li>\n<\/ul>\n<p>As medidas de comprimento indicadas est\u00e3o expressas em metro (m).<\/p>\n<ol>\n<li>Qual das seguintes retas \u00e9 paralela ao plano ADH?<br \/>\n<strong>[A]<\/strong> AB<br \/>\n<strong>[B]<\/strong> IE<br \/>\n<strong>[C]<\/strong> BF<br \/>\n<strong>[D]<\/strong> EG<\/li>\n<li>Sabe-se que \\(IJ = 1\\) m.<br \/>\nDe acordo com os dados da figura, determina o volume da barraca de praia.<br \/>\nApresenta todos os c\u00e1lculos que efetuares e, na tua resposta, indica a unidade de volume.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13949' onClick='GTTabs_show(1,13949)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13949'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13951\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13951\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png\" data-orig-size=\"1005,402\" 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=\"Barraca de praia\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png\" class=\"alignright wp-image-13951\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b-300x120.png\" alt=\"\" width=\"480\" height=\"192\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b-300x120.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b-768x307.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7b.png 1005w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/a>Das alternativas apresentadas, a reta BF \u00e9 a \u00fanica que \u00e9 paralela ao plano ADH (op\u00e7\u00e3o <strong>[C]<\/strong>).<br \/>\n\u00ad<\/li>\n<li>Comecemos por determinar o comprimento, em metros, da altura da pir\u00e2mide, aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [IJK]:<br \/>\n\\[\\begin{array}{*{20}{l}}{\\overline {IK} }&amp; = &amp;{\\sqrt {{{\\overline {IJ} }^2} &#8211; {{\\overline {KJ} }^2}} }\\\\{}&amp; = &amp;{\\sqrt {{1^2} &#8211; {{0,6}^2}} }\\\\{}&amp; = &amp;{\\sqrt {0,64} }\\\\{}&amp; = &amp;{0,8}\\end{array}\\]<br \/>\nA barraca de praia tem 2,832 m<sup>3<\/sup> de volume:<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{Barraca}}}&amp; = &amp;{{V_{Prisma}} + {V_{Pir\u00e2mide}}}\\\\{}&amp; = &amp;{\\left( {\\overline {AB} \\times \\overline {AD} } \\right) \\times \\overline {AE} + \\frac{1}{3} \\times \\left( {\\overline {AB} \\times \\overline {AD} } \\right) \\times \\overline {IK} }\\\\{}&amp; = &amp;{\\left( {1,2 \\times 1,2} \\right) \\times 1,7 + \\frac{1}{3} \\times \\left( {1,2 \\times 1,2} \\right) \\times 0,8}\\\\{}&amp; = &amp;{2,448 + 0,384}\\\\{}&amp; = &amp;{2,832}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13949' onClick='GTTabs_show(0,13949)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na praia do parque de campismo existem barracas como as indicadas na fotografia. Ao lado da fotografia est\u00e1 um esquema da estrutura de uma dessas barracas. Relativamente \u00e0 figura, sabe-se: [ABCDEFGH]&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20409,"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-13949","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":3894,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag039-7_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13949","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=13949"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13949\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20409"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13949"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}