{"id":13491,"date":"2018-02-05T19:39:24","date_gmt":"2018-02-05T19:39:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13491"},"modified":"2022-01-16T15:00:19","modified_gmt":"2022-01-16T15:00:19","slug":"um-cone-de-revolucao-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13491","title":{"rendered":"Um cone de revolu\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_13491' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13491' class='GTTabs_curr'><a  id=\"13491_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13491' ><a  id=\"13491_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_13491'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13493\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13493\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png\" data-orig-size=\"390,215\" 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=\"Cone de revolu\u00e7\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png\" class=\"alignright size-medium wp-image-13493\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4-300x165.png\" alt=\"\" width=\"300\" height=\"165\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4-300x165.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png 390w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Um tri\u00e2ngulo ret\u00e2ngulo [ABC], em que o cateto [AB] est\u00e1 contido no plano\u00a0\\(\\beta \\), rodou em torno do outro cateto gerando um cone, como se mostra na figura.<\/p>\n<p>Sabendo que \\(\\overline {AC} = 4\\) cm e que\u00a0\\(\\overline {AB} = 3\\) cm, determine a dist\u00e2ncia do ponto C ao plano\u00a0\\(\\beta \\).<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13491' onClick='GTTabs_show(1,13491)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13491'>\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\/02\/9V2Pag011-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13493\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13493\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png\" data-orig-size=\"390,215\" 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=\"Cone de revolu\u00e7\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png\" class=\"alignright size-medium wp-image-13493\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4-300x165.png\" alt=\"\" width=\"300\" height=\"165\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4-300x165.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4.png 390w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [ABC], vem:<\/p>\n<p>\\[\\overline {BC} = \\sqrt {{{\\overline {AC} }^2} &#8211; {{\\overline {AB} }^2}} = \\sqrt {{4^2} &#8211; {3^2}} = \\sqrt 7 \\]<\/p>\n<p>Portanto,\u00a0a dist\u00e2ncia do ponto C ao plano\u00a0\\(\\beta \\) \u00e9 \\(\\sqrt 7 \\) cm.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13491' onClick='GTTabs_show(0,13491)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um tri\u00e2ngulo ret\u00e2ngulo [ABC], em que o cateto [AB] est\u00e1 contido no plano\u00a0\\(\\beta \\), rodou em torno do outro cateto gerando um cone, como se mostra na figura. Sabendo que \\(\\overline&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20368,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,467],"series":[],"class_list":["post-13491","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-distancia"],"views":2319,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/02\/9V2Pag011-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13491","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=13491"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13491\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20368"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13491"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13491"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13491"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13491"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}