{"id":23787,"date":"2026-05-20T18:54:06","date_gmt":"2026-05-20T21:54:06","guid":{"rendered":"https:\/\/xequematenem.com.br\/blog\/?p=23787"},"modified":"2026-05-20T18:54:08","modified_gmt":"2026-05-20T21:54:08","slug":"questao-177-enem-2025","status":"publish","type":"post","link":"https:\/\/xequematenem.com.br\/blog\/questao-177-enem-2025\/","title":{"rendered":"Quest\u00e3o 177 &#8211; ENEM 2025"},"content":{"rendered":"\n<p>A figura ilustra o projeto visual para confec\u00e7\u00e3o de uma medalha comemorativa, com a forma de um cilindro circular reto, de di\u00e2metro 6 cm e espessura 3 mm.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"511\" height=\"243\" src=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2026\/05\/image-2.png\" alt=\"\" class=\"wp-image-23788\" title=\"\" srcset=\"https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2026\/05\/image-2.png 511w, https:\/\/xequematenem.com.br\/blog\/wp-content\/uploads\/2026\/05\/image-2-300x143.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/figure>\n\n\n\n<p>A figura ABCD tem a forma de um quadrado e \u00e9 a base de um prisma que atravessa toda a medalha. A regi\u00e3o da medalha externa a esse prisma ser\u00e1 cunhada em ouro. Pretende-se cunhar 100 dessas medalhas.&nbsp;<\/p>\n\n\n\n<p>Considere 3,1 como valor aproximado para p.&nbsp;<\/p>\n\n\n\n<p>Qual \u00e9 o volume de ouro, em cent\u00edmetro c\u00fabico, necess\u00e1rio para a confec\u00e7\u00e3o dessas medalhas?&nbsp;<\/p>\n\n\n\n<p>A) 288&nbsp;<\/p>\n\n\n\n<p>B) 297&nbsp;<\/p>\n\n\n\n<p>C) 567&nbsp;<\/p>\n\n\n\n<p>D) 990&nbsp;<\/p>\n\n\n\n<p>E) 1134&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>Resolu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p>Considere:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>medalha em forma de cilindro;<\/li>\n\n\n\n<li>di\u00e2metro <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>6<\/mn><mtext>&nbsp;cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">6\\text{ cm}<\/annotation><\/semantics><\/math>6\u00a0cm \u2192 raio <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mtext>&nbsp;cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">3\\text{ cm}<\/annotation><\/semantics><\/math>3\u00a0cm;<\/li>\n\n\n\n<li>espessura <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mtext>&nbsp;mm<\/mtext><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>3<\/mn><mtext>&nbsp;cm<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">3\\text{ mm}=0,3\\text{ cm}<\/annotation><\/semantics><\/math>3\u00a0mm=0,3\u00a0cm.<\/li>\n<\/ul>\n\n\n\n<p>O volume total de uma medalha \u00e9:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">V_c=\\pi r^2 h<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mn>3<\/mn><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">V_c=3,1\\cdot 3^2 \\cdot 0,3<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mn>3<\/mn><mo separator=\"true\">,<\/mo><mn>1<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>\u22c5<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">V_c=3,1\\cdot 9 \\cdot 0,3<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>c<\/mi><\/msub><mo>=<\/mo><mn>8<\/mn><mo separator=\"true\">,<\/mo><mn>37<\/mn><msup><mtext>&nbsp;cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V_c=8,37\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>O prisma interno possui base quadrada inscrita no c\u00edrculo de raio 3 cm.<\/p>\n\n\n\n<p>A diagonal do quadrado \u00e9 o di\u00e2metro do c\u00edrculo:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>d<\/mi><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">d=6<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Logo, o lado do quadrado \u00e9:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><mfrac><mn>6<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mfrac><mo>=<\/mo><mn>3<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">l=\\frac{6}{\\sqrt2}=3\\sqrt2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u00c1rea da base do quadrado:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><msqrt><mn>2<\/mn><\/msqrt><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>18<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A=(3\\sqrt2)^2=18<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Volume do prisma:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>V<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><mn>18<\/mn><mo>\u22c5<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mn>3<\/mn><mo>=<\/mo><mn>5<\/mn><mo separator=\"true\">,<\/mo><mn>4<\/mn><msup><mtext>&nbsp;cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">V_p=18\\cdot0,3=5,4\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Volume de ouro em uma medalha:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>8<\/mn><mo separator=\"true\">,<\/mo><mn>37<\/mn><mo>\u2212<\/mo><mn>5<\/mn><mo separator=\"true\">,<\/mo><mn>4<\/mn><mo>=<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mn>97<\/mn><msup><mtext>&nbsp;cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">8,37-5,4=2,97\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>Para 100 medalhas:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>100<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo separator=\"true\">,<\/mo><mn>97<\/mn><mo>=<\/mo><mn>297<\/mn><msup><mtext>&nbsp;cm<\/mtext><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">100\\cdot2,97=297\\text{ cm}^3<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>Alternativa B<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A figura ilustra o projeto visual para confec\u00e7\u00e3o de uma medalha comemorativa, com a forma de um cilindro circular reto, de di\u00e2metro 6 cm e espessura 3 mm.&nbsp; A figura ABCD tem a forma de um quadrado e \u00e9 a base de um prisma que atravessa toda a medalha. A regi\u00e3o da medalha externa a [&hellip;]<\/p>\n","protected":false},"author":23,"featured_media":23788,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17,186],"tags":[],"area-do-conhecimento":[118,132],"assunto":[54],"class_list":["post-23787","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-questoes-do-enem","category-2025-questoes-enem-regular","area-do-conhecimento-matematica-e-suas-tecnologias","area-do-conhecimento-matematica","assunto-geometria-espacial"],"_links":{"self":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/23787","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/users\/23"}],"replies":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/comments?post=23787"}],"version-history":[{"count":1,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/23787\/revisions"}],"predecessor-version":[{"id":23789,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/posts\/23787\/revisions\/23789"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media\/23788"}],"wp:attachment":[{"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/media?parent=23787"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/categories?post=23787"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/tags?post=23787"},{"taxonomy":"area-do-conhecimento","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/area-do-conhecimento?post=23787"},{"taxonomy":"assunto","embeddable":true,"href":"https:\/\/xequematenem.com.br\/blog\/wp-json\/wp\/v2\/assunto?post=23787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}