\u00c0 partir d’une feuille de papier au format A4, on veut construire le patron d’une boite sans\u00a0couvercle qui a la forme d’un parall\u00e9l\u00e9pip\u00e8de rectangle et qui a le plus grand volume possible.<\/p>\r\n
Quelles sont ses dimensions ?<\/p>\r\n
Retour Panier \u00e0 probl\u00e8mes <\/a><\/p>\r\n \u2666 Forme(s) d’un patron d’un parall\u00e9l\u00e9pip\u00e8de rectangle (sans couvercle) * le point critique de cette fonction n’est pas un nombre d\u00e9cimal, les \u00e9l\u00e8ves ne le trouveront pas <\/em>par essais \u00ab \u00e0 la main \u00bb et n’auront qu’une valeur approch\u00e9e avec le tableur. La repr\u00e9sentation <\/em>graphique leur permettra de conjecturer plus facilement le maximum recherch\u00e9<\/em>.<\/p>\r\n T\u00e9l\u00e9charcher le document complet <\/a><\/p>\r\n","protected":false},"excerpt":{"rendered":" Avec une feuille A4, comment construire une bo\u00eete sans couvercle maximisant le volume\u202f?<\/p>\n","protected":false},"author":3,"featured_media":2833,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107],"tags":[],"niveau":[113],"type_situation":[116],"theme_maths":[118,119],"probleme_associe":[],"type-expe":[],"class_list":{"0":"post-2831","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-situation-probleme","8":"niveau-cycle-4","9":"type_situation-situation-probleme","10":"theme_maths-nombres-et-calculs","11":"theme_maths-ogd-fonctions","12":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle-150x149.png",150,149,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle.png",169,149,false],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/LaBoiteSansCouvercle-169x141.png",169,141,true]},"rttpg_author":{"display_name":"St\u00e9phanie CROQUELOIS","author_link":"https:\/\/math.univ-lyon1.fr\/dream\/?author=3"},"rttpg_comment":0,"rttpg_category":"Situation Probl\u00e8me<\/a>","rttpg_excerpt":"Avec une feuille A4, comment construire une bo\u00eete sans couvercle maximisant le volume\u202f?","_links":{"self":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2831","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2831"}],"version-history":[{"count":11,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2831\/revisions"}],"predecessor-version":[{"id":3814,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2831\/revisions\/3814"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/media\/2833"}],"wp:attachment":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2831"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2831"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2831"},{"taxonomy":"niveau","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fniveau&post=2831"},{"taxonomy":"type_situation","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype_situation&post=2831"},{"taxonomy":"theme_maths","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftheme_maths&post=2831"},{"taxonomy":"probleme_associe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fprobleme_associe&post=2831"},{"taxonomy":"type-expe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype-expe&post=2831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Objets potentiellement travaill\u00e9s\/Connaissances en jeu<\/h3>\r\n
\u2666 Formule du volume d’un parall\u00e9l\u00e9pip\u00e8de rectangle et de l’aire d’un rectangle
\u2666 D\u00e9pendance d’une grandeur (le volume) en fonction d’une autre (la hauteur)
\u2666 Production de formules et\/ou de m\u00e9thodes en utilisant le calcul litt\u00e9ral (expression alg\u00e9brique d’une fonction)
\u2666 Utilisation du tableur (tableau de valeurs d’une fonction)
\u2666 Utilisation du grapheur (repr\u00e9sentation graphique d’une fonction)*
\u2666 Calculs de fonctions d\u00e9riv\u00e9es, \u00e9tude du sens de variation et recherche d’extrema locaux
\u2666 R\u00e9solution d’\u00e9quations (second degr\u00e9)<\/p>\r\n