import work from year 2015-2016
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\parbox{0.65\linewidth}{Paul en visite à Paris admire la Pyramide, réalisée en verre feuilleté au centre de la cour intérieure du Louvre.
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Cette pyramide régulière a :
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\setlength\parindent{6mm}
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\begin{itemize}
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\item[$\bullet~~$] pour base un carré ABCD de côté 35 mètres ;
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\item[$\bullet~~$] pour hauteur le segment [SO] de longueur 22 mètres.
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\end{itemize}
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\setlength\parindent{0mm}}
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\hfill
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\parbox{0.3\linewidth}{
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\includegraphics[scale=0.2]{./fig/2014_CE_Exo4_pyramide}
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}
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\medskip
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Paul a tellement apprécié cette pyramide qu'il achète comme souvenir de sa visite une lampe à huile dont le réservoir en verre est une réduction à l'échelle $\dfrac{1}{500}$ de la vraie pyramide.
|
||||
|
||||
Le mode d'emploi de la lampe précise que, une fois allumée, elle brûle 4 cm$^3$ d'huile par heure.
|
||||
|
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Au bout de combien de temps ne restera-t-il plus d'huile dans le réservoir ? Arrondir à l'unité d'heures.
|
||||
|
||||
\textbf{Rappel :} \emph{Volume d'une pyramide = un tiers du produit de l'aire de la base par la hauteur}
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|
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\medskip
|
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|
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\textbf{Faire apparaitre sur la copie la démarche utilisée. Toute trace de recherche sera prise en compte lors de l'évaluation même si le travail n'est pas complètement abouti.}
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Pour amortir les chocs contre les autres embarcations ou le quai, les péniches sont équipées de \og boudins \fg{} de protection.
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\parbox{0.48\linewidth}{
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\includegraphics[scale=0.2]{./fig/2014_juin_AN_Exo2}
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}\hfill
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\parbox{0.48\linewidth}{
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\begin{enumerate}
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\item Calculer le volume exact en cm$^3$ du \og boudin \fg de protection ci-contre, puis arrondir au centième.
|
||||
\item On veut réaliser une bouée deux fois plus grande. Quelle sera son volume?
|
||||
\item On veut réaliser une bouée qui serait réduite d'un rapport 0.4. Quelle sera son volume?
|
||||
\end{enumerate}
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}
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\textbf{Rappel}
|
||||
|
||||
\textbf{Volume d'un cylindre de révolution} $V = \pi R^2 h$ où $h$ désigne la hauteur du cylindre et $R$ le rayon de la base.
|
||||
|
||||
\textbf{Volume d'une boule} $V = \dfrac{4}{3}\pi R^3$ où $R$ désigne le rayon de la boule.
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\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
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% Title Page
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\titre{Agrandissement aire et volumes - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Mai 2016}
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\pagestyle{empty}
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\begin{document}
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\begin{Exo}
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\input{./2014_juin_AN_exo2.tex}
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\end{Exo}
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\begin{Exo}
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\input{./2014_CE_exo4.tex}
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\end{Exo}
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\pagebreak
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\setcounter{exo}{0}
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\begin{Exo}
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\input{./2014_juin_AN_exo2.tex}
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\end{Exo}
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\begin{Exo}
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\input{./2014_CE_exo4.tex}
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\end{Exo}
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\pagebreak
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\setcounter{exo}{0}
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\end{document}
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26
3e/Unites_et_grandeurs/Agrandissement_aire_volume/index.rst
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Notes sur le chapitre agrandissement des aires et des volumes pour les 3e
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#########################################################################
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||||
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||||
:date: 2016-05-30
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||||
:modified: 2016-07-06
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||||
:tags: Agrandissement, volume, aire
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:category: 3e
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||||
:authors: Bertrand Benjamin
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||||
:summary: Chapitre sur les agrandissement et les réductions des aires et des volumes pour les 3e.
|
||||
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||||
Objectifs
|
||||
=========
|
||||
|
||||
- Revoir les calculs d'aires et de volumes
|
||||
- Découvrir comment se comportent l'aire et le volumes lors d'un agrandissement.
|
||||
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||||
Déroulement
|
||||
===========
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||||
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||||
- Séance 1-2: J'ai repris une activité de Sesamath. On veut faire un miniature d'un immeuble (un pavé droit) dont les dimensions sont données. J'ai partagé la classe en 4 parties, chaque partie devait calculer les dimensions de la miniature suivant différentes échelles. Une fois les dimensions calculées, on calculait la surface au sol ainsi que le volume du vrai immeuble et de la miniature.
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||||
On a ensuite tracé ces `graphiques <./graphs_echelles.pdf>`_ pour se rendre compte que l'évolution n'était pas toujours linéaire. *Ces graphiques en fait ne sont pas très révélateurs... Il faudrait faire le graphique en comparant les dimensions de plusieurs objets en fonction d'une seule échelle. Ce serait plus juste*.
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On peut ensuite écrire le cours où on explique que quand on agrandit d'un facteur *k* l'aire est multipliée par k^2 et le volume par k^3.
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- Les autres séances sont consacrées à cette `fiche d'exercices <./exo_agrandissement.pdf>`_.
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3817
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