{"id":13739,"date":"2018-03-03T19:45:18","date_gmt":"2018-03-03T19:45:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13739"},"modified":"2022-01-16T17:12:36","modified_gmt":"2022-01-16T17:12:36","slug":"um-tronco-de-cone","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13739","title":{"rendered":"Um tronco de cone"},"content":{"rendered":"<p><ul id='GTTabs_ul_13739' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13739' class='GTTabs_curr'><a  id=\"13739_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13739' ><a  id=\"13739_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_13739'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13740\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13740\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png\" data-orig-size=\"480,250\" 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 cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png\" class=\"alignright wp-image-13740\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6-300x156.png\" alt=\"\" width=\"400\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6-300x156.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png 480w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Considera a figura.<\/p>\n<ol>\n<li>Qual \u00e9 o valor de x?<\/li>\n<li>Calcula, apresentando o resultado arredondado \u00e0s cent\u00e9simas, o volume:<br \/>\na) do cone maior;<br \/>\nb) do cone menor;<br \/>\nc) do troco de cone.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13739' onClick='GTTabs_show(1,13739)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13739'>\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\/9V2Pag21-6.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13740\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13740\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png\" data-orig-size=\"480,250\" 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 cone\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png\" class=\"alignright wp-image-13740\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6-300x156.png\" alt=\"\" width=\"400\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6-300x156.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag21-6.png 480w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>De acordo com os dados assinalados na figura, tem-se:\u00a0\\(x = 20 &#8211; 15 = 5\\) cm.<\/p>\n<p>Apresentam-se, seguidamente, os volumes pedidos, em cent\u00edmetros c\u00fabicos, com arredondamento \u00e0s cent\u00e9simas.<\/p>\n<p><strong>Volume do cone maior<\/strong>:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{V_{CONEmaior}}}&amp; = &amp;{\\frac{1}{3} \\times \\pi \\times {8^2} \\times 20}\\\\{}&amp; = &amp;{\\frac{{1280\\pi }}{3}}\\\\{}&amp; \\approx &amp;{1340,41}\\end{array}\\]<\/p>\n<p><strong>Volume do cone menor<\/strong>:<\/p>\n<p>Comecemos por determinar o raio da base do cone menor, tendo em considera\u00e7\u00e3o a semelhan\u00e7a de tri\u00e2ngulos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{r}{8} = \\frac{5}{{20}}}&amp; \\Leftrightarrow &amp;{r = \\frac{{8 \\times 5}}{{20}}}\\\\{}&amp; \\Leftrightarrow &amp;{r = 2}\\end{array}\\]<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{V_{CONEmenor}}}&amp; = &amp;{\\frac{1}{3} \\times \\pi \\times {2^2} \\times 5}\\\\{}&amp; = &amp;{\\frac{{20\\pi }}{3}}\\\\{}&amp; \\approx &amp;{20,94}\\end{array}\\]<\/p>\n<p><strong>Volume do tronco de cone<\/strong>:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{V_{TroncoCONE}}}&amp; = &amp;{{V_{CONEmaior}} &#8211; {V_{CONEmenor}}}\\\\{}&amp; = &amp;{\\frac{{1280\\pi }}{3} &#8211; \\frac{{20\\pi }}{3}}\\\\{}&amp; = &amp;{420\\pi }\\\\{}&amp; \\approx &amp;{1319,47}\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13739' onClick='GTTabs_show(0,13739)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considera a figura. Qual \u00e9 o valor de x? Calcula, apresentando o resultado arredondado \u00e0s cent\u00e9simas, o volume: a) do cone maior; b) do cone menor; c) do troco de cone.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20388,"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-13739","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":3503,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag021-6_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13739","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=13739"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13739\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20388"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13739"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}