{"id":13877,"date":"2018-03-07T17:29:55","date_gmt":"2018-03-07T17:29:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13877"},"modified":"2022-01-16T19:08:29","modified_gmt":"2022-01-16T19:08:29","slug":"uma-piramide-de-madeira","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13877","title":{"rendered":"Uma pir\u00e2mide de madeira"},"content":{"rendered":"<p><ul id='GTTabs_ul_13877' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13877' class='GTTabs_curr'><a  id=\"13877_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13877' ><a  id=\"13877_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_13877'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13878\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13878\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png\" data-orig-size=\"480,325\" 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=\"Tronco de pir\u00e2mide\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png\" class=\"alignright wp-image-13878\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b-300x203.png\" alt=\"\" width=\"400\" height=\"271\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b-300x203.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png 480w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>A base de uma pir\u00e2mide de madeira \u00e9 um quadrado com 10 cm de lado.\u00a0A 5 cm do v\u00e9rtice da pir\u00e2mide fez-se um corte paralelo \u00e0 base. Com isso, obteve-se uma nova pir\u00e2mide cujo lado do pol\u00edgono da base mede 2 cm e um tronco de pir\u00e2mide, como mostra a figura.<\/p>\n<p>Determina o volume do tronco de pir\u00e2mide.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13877' onClick='GTTabs_show(1,13877)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13877'>\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\/9V2Pag032-10b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13878\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13878\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png\" data-orig-size=\"480,325\" 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=\"Tronco de pir\u00e2mide\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png\" class=\"alignright wp-image-13878\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b-300x203.png\" alt=\"\" width=\"400\" height=\"271\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b-300x203.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10b.png 480w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>As duas pir\u00e2mides consideradas s\u00e3o semelhantes, sendo a pir\u00e2mide inicial uma amplia\u00e7\u00e3o da nova pir\u00e2mide com raz\u00e3o de semelhan\u00e7a\u00a0\\(r = \\frac{{10}}{2} = 5\\).<\/p>\n<p>Quanto \u00e0 nova pir\u00e2mide, o seu volume \u00e9\u00a0\\({V_{PNova}} = \\frac{1}{3} \\times {2^2} \\times 5 = \\frac{{20}}{3}\\) cm<sup>3<\/sup>.<br \/>\n\u00ad<\/p>\n<p>Como\u00a0\\(\\frac{{{V_{PInicial}}}}{{{V_{PNova}}}} = {r^3} = {5^3} = 125\\), ent\u00e3o\u00a0\\({V_{PInicial}} = 125 \\times \\frac{{20}}{3} = \\frac{{2500}}{3}\\) cm<sup>3<\/sup>.<br \/>\n\u00ad<\/p>\n<p>Assim, temos:\u00a0\\({V_{Tronco}} = {V_{PInicial}} &#8211; {V_{PNova}} = \\frac{{2500}}{3} &#8211; \\frac{{20}}{3} = \\frac{{2480}}{3}\\) cm<sup>3<\/sup>.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13877' onClick='GTTabs_show(0,13877)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A base de uma pir\u00e2mide de madeira \u00e9 um quadrado com 10 cm de lado.\u00a0A 5 cm do v\u00e9rtice da pir\u00e2mide fez-se um corte paralelo \u00e0 base. Com isso, obteve-se uma&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20406,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,471,486,109],"series":[],"class_list":["post-13877","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-tronco-de-piramide","tag-volume"],"views":3023,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag032-10_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13877","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=13877"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13877\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20406"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13877"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}