{"id":2266,"date":"2020-04-22T10:42:19","date_gmt":"2020-04-22T10:42:19","guid":{"rendered":"http:\/\/alexandrewack.fr\/?page_id=2266"},"modified":"2020-04-22T13:58:18","modified_gmt":"2020-04-22T13:58:18","slug":"longueurs-developpees","status":"publish","type":"page","link":"http:\/\/alexandrewack.fr\/?page_id=2266","title":{"rendered":"Longueurs d\u00e9velopp\u00e9es"},"content":{"rendered":"\n

RAPPEL<\/strong>: <\/p>\n\n\n\n

Calcul du p\u00e9rim\u00e8tre d’un cercle :<\/strong> au programme de CM2

Pour calculer le p\u00e9rim\u00e8tre du cercle, on va utiliser son rayon ou le diam\u00e8tre , et un nombre qui s\u2019appelle pi que l’on \u00e9crit ( \u03c0 )<\/strong> et qui a comme valeur 3,14.<\/strong> <\/p>\n\n\n\n

P\u00e9rim\u00e8tre est \u00e9gale \u00e0:

P = \u03c0 x \u00d8

ou

P = \u03c0 x Raillon x 2 <\/strong><\/p>\n\n\n\n

Pour calculer la circonf\u00e9rence (p\u00e9rim\u00e8tre) si nous utilisons le rayon , du cercle, on applique la formule suivante:
      Circonf\u00e9rence (p\u00e9rim\u00e8tre) = (r X 2) X  \u03c0<\/strong>
<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Pour calculer la circonf\u00e9rence (p\u00e9rim\u00e8tre) si nous utilisons le diam\u00e8tre , du cercle, on applique la formule suivante:
      Circonf\u00e9rence (p\u00e9rim\u00e8tre) = (diam\u00e8tre) D X  \u03c0<\/strong> <\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Dans n\u00f4tre cas le cercle poss\u00e8de une \u00e9paisseur donc : <\/strong><\/p>\n\n\n\n

le roulage de t\u00f4le :<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n
\"\"<\/figure><\/div>\n\n\n\n

La longueur de la fibre neutre situ\u00e9e \u00e0 la moiti\u00e9s de l\u2019\u00e9paisseur de la t\u00f4le.
Elle reste invariable.
Pour un cylindre, on calcule la longueur d\u00e9velopp\u00e9e en consid\u00e9rant le diam\u00e8tre (moyen) \u00e0 la fibre neutre. <\/p>\n\n\n\n

Ld => longueur d\u00e9velopp\u00e9e <\/p>\n\n\n\n

Ld = \u03c0 x \u00d8fn <\/strong><\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Pour calculer la longueur de la t\u00f4le \u00e0 plat (d\u00e9velopp\u00e9e) , 3 possibilit\u00e9s : <\/strong><\/p>\n\n\n\n


Ld = \u03c0 x \u00d8fn <\/strong> \u00d8fn => Diam\u00e8tre en fibre neutre 

Ld = \u03c0 x (\u00d8int + ep.)<\/strong> \u00d8int => Diam\u00e8tre int\u00e9rieur

Ld = \u03c0 x (\u00d8ext \u2013 ep.) <\/strong> \u00d8ext => Diam\u00e8tre ext\u00e9rieur
<\/p>\n\n\n\n

Exemple :<\/strong><\/p>\n\n\n\n

Si on souhaite obtenir une virole de diam\u00e8tre ext\u00e9rieur 500 mm en \u00e9paisseur 4 mm et de 1000 mm de hauteur : <\/p>\n\n\n\n

Ld = \u03c0 x \u00d8fn (avec \u00d8fn= \u00d8ext \u2013 ep)
Ld = \u03c0 x (500 -4)
LD = \u03c0 x 495 ==> LD \u2248 1555,08 <\/strong>

<\/p>\n\n\n\n

On devra donc d\u00e9couper un rectangle de t\u00f4le de :

1000 mm x 1555 mm avant roulage. <\/strong><\/p>\n\n\n\n

Pour v\u00e9rifier les calculs : http:\/\/www.echoumac.com\/html\/virole-rev0.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

RAPPEL: Calcul du p\u00e9rim\u00e8tre d’un cercle : au programme de CM2 Pour calculer le p\u00e9rim\u00e8tre du cercle, on va utiliser son rayon ou le diam\u00e8tre , et un nombre qui s\u2019appelle pi que l’on \u00e9crit ( \u03c0 ) et qui a comme valeur 3,14. P\u00e9rim\u00e8tre est \u00e9gale \u00e0: P = \u03c0 x \u00d8 ou P […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":280,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2266","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/pages\/2266","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2266"}],"version-history":[{"count":31,"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/pages\/2266\/revisions"}],"predecessor-version":[{"id":2317,"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/pages\/2266\/revisions\/2317"}],"up":[{"embeddable":true,"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=\/wp\/v2\/pages\/280"}],"wp:attachment":[{"href":"http:\/\/alexandrewack.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}