Solides

Pour aller plus loin (Ancien programme) - Mathématiques 4e

Exercice 1 : Calcul du volume d'un prisme droit

Soit un prisme droit de \(1 cm\) de hauteur. Ses bases sont des triangles dont l'un des côtés mesure \(1 cm\) et dont la hauteur relative à ce côté est de \(4 cm\).

Calculer son volume.
On donnera la réponse suivie de l'unité qui convient.

Exercice 2 : Reconnaître le patron d'un pavé droit

Soit le pavé suivant :

Parmi les figures suivantes, trouver celle ou celles étant un patron de ce pavé.

Exercice 3 : Lire latitude ou longitude d'une ville sur terre à partir des angles

Sur le schéma ci-dessous, le point D symbolise la ville de Sultanbeyli (Turquie).

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14.635618599362983}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": -26.403354881189486, "y": 26.24236115962029, "z": 14.635618599362983}, "text": "D", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 16711680}}}}

On pourra faire pivoter la figure en cliquant dessus.

Légende

Méridien d'origine Greenwich 0°
Méridien du point D
Équateur 0°
Parallèle du point D
N : Pôle nord
S : Pôle sud
C : Centre de la terre
D : Ville de Sultanbeyli

Sachant que \( \widehat{DCN} = 49 ° \), \( \widehat{SCE} = 90 ° \), \( \widehat{ABD} = 29 ° \) et \( \widehat{ECD} = 41 ° \), donner la latitude de la ville de Sultanbeyli (Turquie).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)

Exercice 4 : Calcul du volume d'un cylindre de révolution

Soit un cylindre de révolution de \( 3 cm \) de hauteur et de \( 6 cm \) de rayon.

Calculer son volume.
On donnera le résultat exact.

Exercice 5 : Convertir des aires (multiples et sous-multiples du m^2)

Convertir \( 0,04\:\text{cm}^{2} \) en \( \text{mm}^{2} \).
On écrira la réponse sous la forme d'un entier ou d'un nombre décimal non entier.

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