{"id":4967,"date":"2010-10-31T18:29:13","date_gmt":"2010-10-31T18:29:13","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4967"},"modified":"2022-01-19T14:10:20","modified_gmt":"2022-01-19T14:10:20","slug":"num-acampamento","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4967","title":{"rendered":"Num acampamento"},"content":{"rendered":"<p><ul id='GTTabs_ul_4967' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4967' class='GTTabs_curr'><a  id=\"4967_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4967' ><a  id=\"4967_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_4967'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4968\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4968\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg\" data-orig-size=\"466,263\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Tenda\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg\" class=\"alignright wp-image-4968\" title=\"Tenda\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-300x169.jpg\" alt=\"\" width=\"300\" height=\"169\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-300x169.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-150x84.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-400x225.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg 466w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Num acampamento utiliza-se uma tenda c\u00f3nica, cuja base \u00e9 um c\u00edrculo com 4 m de di\u00e2metro e cujo volume \u00e9 15,072 m<sup>3<\/sup>.<\/p>\n<p>Qual \u00e9 a altura da tenda?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4967' onClick='GTTabs_show(1,4967)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4967'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4968\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4968\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg\" data-orig-size=\"466,263\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Tenda\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg\" class=\"alignright wp-image-4968\" title=\"Tenda\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-300x169.jpg\" alt=\"\" width=\"300\" height=\"169\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-300x169.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-150x84.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2-400x225.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/tenda2.jpg 466w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Como o di\u00e2metro da base \u00e9 4 m, ent\u00e3o o raio tem 2 m de comprimento.<\/p>\n<p>Como sabemos, o volume de um cone, com raio da base r e altura h, \u00e9 dado por: \\[{{V}_{c}}=\\frac{1}{3}\\times {{A}_{b}}\\times h=\\frac{1}{3}\\times \\pi \\times {{r}^{2}}\\times h\\]<\/p>\n<p>Substituindo os valores conhecidos nessa express\u00e3o, obt\u00e9m-se: \\[15,072=\\frac{1}{3}\\times \\pi \\times {{2}^{2}}\\times h\\]<\/p>\n<p>Donde, \\[\\begin{array}{*{35}{l}}<br \/>\n15,072=\\frac{1}{3}\\times \\pi \\times {{2}^{2}}\\times h &amp; \\Leftrightarrow\u00a0 &amp; \\frac{1}{3}\\times \\pi \\times {{2}^{2}}\\times h=15,072\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{4\\pi }{3}\\times h=15,072\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 4\\pi \\times h=45,216\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; h=\\frac{45,216}{4\\pi }\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; h=\\frac{11,304}{\\pi }\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Logo, a altura da tenda \u00e9, aproximadamente, $h\\simeq 3,6\\,m$.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4967' onClick='GTTabs_show(0,4967)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num acampamento utiliza-se uma tenda c\u00f3nica, cuja base \u00e9 um c\u00edrculo com 4 m de di\u00e2metro e cujo volume \u00e9 15,072 m3. Qual \u00e9 a altura da tenda? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20637,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,67,109],"series":[],"class_list":["post-4967","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-geometria","tag-volume"],"views":2004,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag117-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4967","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=4967"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4967\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20637"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4967"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4967"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4967"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4967"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}