{"id":4960,"date":"2010-10-31T16:54:10","date_gmt":"2010-10-31T16:54:10","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4960"},"modified":"2022-01-14T23:30:40","modified_gmt":"2022-01-14T23:30:40","slug":"o-volume-de-um-cone","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4960","title":{"rendered":"O volume de um cone"},"content":{"rendered":"<p><ul id='GTTabs_ul_4960' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4960' class='GTTabs_curr'><a  id=\"4960_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4960' ><a  id=\"4960_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_4960'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O volume de um cone \u00e9\u00a0942 cm<sup>3<\/sup> e o raio da base mede 10 cm.<\/p>\n<p>Quanto mede a altura do cone?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4960' onClick='GTTabs_show(1,4960)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4960'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"float: right;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":294,\r\n\"height\":340,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/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: \\[942=\\frac{1}{3}\\times \\pi \\times {{10}^{2}}\\times h\\]<\/p>\n<p>Donde, \\[\\begin{array}{*{35}{l}}<br \/>\n942=\\frac{1}{3}\\times \\pi \\times {{10}^{2}}\\times h &amp; \\Leftrightarrow\u00a0 &amp; \\frac{1}{3}\\times \\pi \\times 100\\times h=942\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{100\\pi }{3}\\times h=942\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 100\\pi \\times h=2826\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; h=\\frac{2826}{100\\pi }\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; h=\\frac{1413}{50\\pi }\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Logo, a altura do cone \u00e9, aproximadamente, $h\\simeq 9\\,cm$.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4960' onClick='GTTabs_show(0,4960)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O volume de um cone \u00e9\u00a0942 cm3 e o raio da base mede 10 cm. Quanto mede a altura do cone? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":13797,"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-4960","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":2478,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/cone.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4960","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=4960"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4960\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/13797"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4960"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}