{"id":23185,"date":"2022-11-19T16:32:42","date_gmt":"2022-11-19T16:32:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23185"},"modified":"2022-11-24T19:21:34","modified_gmt":"2022-11-24T19:21:34","slug":"objetos-em-caixas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23185","title":{"rendered":"Objetos em caixas"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23185' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23185' class='GTTabs_curr'><a  id=\"23185_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23185' ><a  id=\"23185_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_23185'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23186\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23186\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png\" data-orig-size=\"400,245\" 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=\"8_Pag056-T8-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png\" class=\"alignright wp-image-23186\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1-300x184.png\" alt=\"\" width=\"340\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1-300x184.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png 400w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Observa a figura onde est\u00e1 representada uma caixa transparente, com a forma de um paralelep\u00edpedo ret\u00e2ngulo, contendo uma caneta.<\/p>\n<ol>\n<li>Usando letras da figura, indica:<br \/>\u00a0&#8211; Duas retas paralelas;<br \/>\u00a0&#8211; Duas retas concorrentes n\u00e3o perpendiculares;<br \/>\u00a0&#8211; Duas retas perpendiculares.<\/li>\n<li>Calcula, arredondado \u00e0s d\u00e9cimas, o comprimento da sombra que a caneta projeta no fundo da caixa.<\/li>\n<li>A Marta pretende substituir a caneta por outra que mede 10 cm. Ser\u00e1 que esta cabe na caixa?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23185' onClick='GTTabs_show(1,23185)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23185'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23186\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23186\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png\" data-orig-size=\"400,245\" 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=\"8_Pag056-T8-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png\" class=\"alignright wp-image-23186\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1-300x184.png\" alt=\"\" width=\"340\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1-300x184.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1.png 400w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Observa a figura onde est\u00e1 representada uma caixa transparente, com a forma de um paralelep\u00edpedo ret\u00e2ngulo, contendo uma caneta.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>Usando letras da figura, indica:<br \/>\u00a0&#8211; Duas retas paralelas;<br \/>\u00a0&#8211; Duas retas concorrentes n\u00e3o perpendiculares;<br \/>\u00a0&#8211; Duas retas perpendiculares.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Calcula, arredondado \u00e0s d\u00e9cimas, o comprimento da sombra que a caneta projeta no fundo da caixa.<\/blockquote>\n<\/li>\n<li>\n<blockquote>A Marta pretende substituir a caneta por outra que mede 10 cm. Ser\u00e1 que esta cabe na caixa?<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li><br \/>\u00a0&#8211; Duas retas paralelas: AC e FH, por exemplo;<br \/>\u00a0&#8211; Duas retas concorrentes n\u00e3o perpendiculares: AE e DF, por exemplo;<br \/>\u00a0&#8211; Duas retas perpendiculares: CH e FH, por exemplo.<br \/><br \/><\/li>\n<li>O comprimento da sombra, em cent\u00edmetros, que a caneta projeta no fundo da caixa, \u00e9:<br \/>\\[\\begin{array}{*{20}{l}}{{C_{sfc}}}&amp; = &amp;{\\overline {EG} }\\\\{}&amp; = &amp;{\\sqrt {{{\\overline {EF} }^2} + {{\\overline {FG} }^2}} }\\\\{}&amp; = &amp;{\\sqrt {{4^2} + {7^2}} }\\\\{}&amp; = &amp;{\\sqrt {16 + 49} }\\\\{}&amp; = &amp;{\\sqrt {65} }\\\\{}&amp; \\approx &amp;{8,1}\\end{array}\\]<br \/><br \/><\/li>\n<li>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [DEG], temos:<br \/>\\[\\begin{array}{*{20}{l}}{\\overline {DG} }&amp; = &amp;{\\sqrt {{{\\overline {DE} }^2} + {{\\overline {EG} }^2}} }\\\\{}&amp; = &amp;{\\sqrt {{5^2} + {{\\left( {\\sqrt {65} } \\right)}^2}} }\\\\{}&amp; = &amp;{\\sqrt {25 + 65} }\\\\{}&amp; = &amp;{\\sqrt {90} }\\end{array}\\]<br \/>N\u00e3o, a caneta que mede 10 cm n\u00e3o cabe na caixa, pois a diagonal espacial da caixa tem menor comprimento do que a caneta, visto que \\(\\sqrt {90} &lt; \\sqrt {100} \\) (e \\(\\sqrt {100} = 10\\)).<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23185' onClick='GTTabs_show(0,23185)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura onde est\u00e1 representada uma caixa transparente, com a forma de um paralelep\u00edpedo ret\u00e2ngulo, contendo uma caneta. Usando letras da figura, indica:\u00a0&#8211; Duas retas paralelas;\u00a0&#8211; Duas retas concorrentes n\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23188,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,118],"series":[],"class_list":["post-23185","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":242,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/11\/8_Pag056-T8-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23185","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=23185"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23185\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23188"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23185"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}