{"id":13749,"date":"2018-03-03T21:35:50","date_gmt":"2018-03-03T21:35:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13749"},"modified":"2022-01-16T17:30:33","modified_gmt":"2022-01-16T17:30:33","slug":"duas-esculturas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13749","title":{"rendered":"Duas esculturas"},"content":{"rendered":"<p><ul id='GTTabs_ul_13749' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13749' class='GTTabs_curr'><a  id=\"13749_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13749' ><a  id=\"13749_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_13749'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13750\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13750\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png\" data-orig-size=\"575,280\" 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=\"Esculturas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png\" class=\"alignright wp-image-13750\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2-300x146.png\" alt=\"\" width=\"400\" height=\"195\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2-300x146.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png 575w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>Observa as esculturas.<\/p>\n<ol>\n<li>Determina um valor arredondado \u00e0s d\u00e9cimas do volume de cada uma delas.<\/li>\n<li>Qual \u00e9 a quantidade de ferro gasta em cada uma das esculturas, sabendo que s\u00e3o maci\u00e7as e que o ferro usado tem uma massa vol\u00famica de 7,8 g\/cm<sup>3<\/sup>.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13749' onClick='GTTabs_show(1,13749)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13749'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13750\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13750\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png\" data-orig-size=\"575,280\" 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=\"Esculturas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png\" class=\"alignright wp-image-13750\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2-300x146.png\" alt=\"\" width=\"400\" height=\"195\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2-300x146.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag22-2.png 575w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>A escultura (A) tem, aproximadamente, 2965,7 mm<sup>3<\/sup> de volume:<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{\\left( A \\right)}}}&amp; = &amp;{{V_{Cilindro}} + \\frac{1}{2}{V_{Esfera}}}\\\\{}&amp; = &amp;{\\pi \\times {4^2} \\times 50 + \\frac{1}{2} \\times \\frac{4}{3}\\pi \\times {6^3}}\\\\{}&amp; = &amp;{800\\pi + 144\\pi }\\\\{}&amp; = &amp;{944\\pi }\\\\{}&amp; \\approx &amp;{2965,7}\\end{array}\\]<br \/>\nA escultura (B) tem, aproximadamente, 171,7 cm<sup>3<\/sup> de volume:<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{\\left( B \\right)}}}&amp; = &amp;{{V_{Cilindro}} + {V_{Esfera}}}\\\\{}&amp; = &amp;{\\pi \\times {2^2} \\times 11 + \\frac{4}{3}\\pi \\times {2^3}}\\\\{}&amp; = &amp;{44\\pi + \\frac{{32\\pi }}{3}}\\\\{}&amp; = &amp;{\\frac{{164\\pi }}{3}}\\\\{}&amp; \\approx &amp;{171,7}\\end{array}\\]<br \/>\n\u00ad<\/li>\n<li>As quantidades de ferro\u00a0gastas em cada uma das esculturas s\u00e3o aproximadamente as seguintes:<br \/>\n\\[{M_{\\left( A \\right)}} = 0,944{\\pi ^{c{m^3}}} \\times {7,8^{g\/c{m^3}}} \\approx {23^g}\\]<br \/>\n\\[{M_{\\left( B \\right)}} = {\\frac{{164\\pi }}{3}^{c{m^3}}} \\times {7,8^{g\/c{m^3}}} \\approx {1340^g}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13749' onClick='GTTabs_show(0,13749)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa as esculturas. Determina um valor arredondado \u00e0s d\u00e9cimas do volume de cada uma delas. Qual \u00e9 a quantidade de ferro gasta em cada uma das esculturas, sabendo que s\u00e3o maci\u00e7as&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20390,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,466],"tags":[426,469,482,109],"series":[],"class_list":["post-13749","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-esfera","tag-volume"],"views":2291,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag022-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13749","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=13749"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13749\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20390"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13749"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13749"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13749"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13749"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}