{"id":13753,"date":"2018-03-03T22:15:27","date_gmt":"2018-03-03T22:15:27","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13753"},"modified":"2022-01-16T18:09:08","modified_gmt":"2022-01-16T18:09:08","slug":"o-volume-de-um-lapis","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13753","title":{"rendered":"O volume de um l\u00e1pis"},"content":{"rendered":"<p><ul id='GTTabs_ul_13753' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13753' class='GTTabs_curr'><a  id=\"13753_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13753' ><a  id=\"13753_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_13753'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcula o volume do l\u00e1pis representado a seguir.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13754\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13754\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png\" data-orig-size=\"475,115\" 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=\"L\u00e1pis\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png\" class=\"aligncenter wp-image-13754 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png\" alt=\"\" width=\"475\" height=\"115\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png 475w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3-300x73.png 300w\" sizes=\"auto, (max-width: 475px) 100vw, 475px\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13753' onClick='GTTabs_show(1,13753)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13753'>\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\/9V2Pag22-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13754\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13754\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png\" data-orig-size=\"475,115\" 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=\"L\u00e1pis\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png\" class=\"alignright wp-image-13754\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3-300x73.png\" alt=\"\" width=\"400\" height=\"97\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3-300x73.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-3.png 475w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Comecemos por determinar a altura do cone, por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras:\u00a0\\(h = \\sqrt {{{1,5}^2} &#8211; {{0,35}^2}} = \\sqrt {2,1275} \\) cm.<\/p>\n<p>Em cent\u00edmetros c\u00fabicos e com aproxima\u00e7\u00e3o \u00e0s cent\u00e9simas, o volume do l\u00e1pis \u00e9 o seguinte:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}V&amp; = &amp;{{V_{Cone}} + {V_{Cilindro}} + \\frac{1}{2}{V_{Esfera}}}\\\\{}&amp; = &amp;{\\frac{1}{3} \\times \\pi \\times {{0,35}^2} \\times \\sqrt {2,1275} + \\pi \\times {{0,35}^2} \\times 10 + \\frac{1}{2} \\times \\frac{4}{3}\\pi \\times {{0,35}^3}}\\\\{}&amp; = &amp;{\\pi \\times {{0,35}^2} \\times \\left( {\\frac{{\\sqrt {2,1275} }}{3} + 10 + \\frac{{0,7}}{3}} \\right)}\\\\{}&amp; = &amp;{\\pi \\times {{0,35}^2} \\times \\frac{{30,7 + \\sqrt {2,1275} }}{3}}\\\\{}&amp; \\approx &amp;{4,13}\\end{array}\\]<\/p>\n<p>Confirma\u00e7\u00e3o do c\u00e1lculo:\u00a0<a href=\"https:\/\/www.wolframalpha.com\/input\/?i=(pi%2F3)*.35%5E2*sqrt(2.1275)%2Bpi*.35%5E2*10%2B(2*Pi%2F3)*.35%5E3\" target=\"_blank\" rel=\"noopener\">Aqui<\/a><\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13753' onClick='GTTabs_show(0,13753)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o volume do l\u00e1pis representado a seguir. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20392,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,469,470,482,109],"series":[],"class_list":["post-13753","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-cilindro","tag-cone","tag-esfera","tag-volume"],"views":2755,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag022-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13753","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=13753"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13753\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20392"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13753"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}