Géométrie dans l'espace
Pour aller plus loin (Ancien programme) - Mathématiques 5e
Exercice 1 : Lire les coordonnées géographique d'une ville sur terre à partir des parallèles et méridiens
Sur le schéma ci-dessous, le point D symbolise la ville de Quevedo (Équateur).
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On pourra faire pivoter la figure en cliquant dessus.
Légende
- Méridien d'origine Greenwich 0°
- Méridiens (espacés de 20°)
- Équateur 0°
- Parallèles (espacés de 20°)
- N : Pôle nord
- S : Pôle sud
- D : Ville de Quevedo
Donner les coordonnées géographique de la ville de Quevedo (Équateur).
Par exemple:
Par exemple:
- Pour la ville de Netanya (Israël) on donnera une réponse de la forme \(\left(32° N; 35° E\right)\)
- Pour la ville de Khammam (Inde) on donnera une réponse de la forme \(\left(17° N; 80° E\right)\)
Exercice 2 : Lire latitude ou longitude d'une ville sur terre à partir des parallèles et méridiens
Sur le schéma ci-dessous, le point D symbolise la ville de Morioka (Japon).
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On pourra faire pivoter la figure en cliquant dessus.
Légende
- Méridien d'origine Greenwich 0°
- Méridiens (espacés de 20°)
- Équateur 0°
- Parallèles (espacés de 20°)
- N : Pôle nord
- S : Pôle sud
- D : Ville de Morioka
Donner la latitude de la ville de Morioka (Japon).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exercice 3 : Calculer la longueur de l'équateur ou d'un méridien à partir du rayon/diamètre de la planète
Sur une planète de diamètre \( 3\:400\:\text{km} \), on définit l'équateur de la même manière que sur Terre.
Quelle est la longueur de l'équateur de cette planète ?
On arrondira le résultat au kilomètre près, suivi de l'unité qui convient.
On arrondira le résultat au kilomètre près, suivi de l'unité qui convient.
Exercice 4 : 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 San Juan (Argentine).
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-31.668844131994245}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": -12.156530293414963, "y": -21.196770569328194, "z": -31.668844131994245}, "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 San Juan
Sachant que \( \widehat{SCE} = 90 ° \), \( \widehat{ECD} = 32 ° \), \( \widehat{DCN} = 122 ° \) et \( \widehat{ABD} = 69 ° \), donner la latitude de la ville de San Juan (Argentine).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exercice 5 : Calculer le rayon d'un parallèle
On assimile la Terre à une sphère de rayon \( 6\:400\:\text{km} \).
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On pourra faire pivoter la figure en cliquant dessus.
Légende
- Équateur 0°
- Parallèle passant par D
- N : Pôle nord
- S : Pôle sud
- D : Ville de Kasūr
Déterminer le rayon du parallèle passant à Kasūr de coordonnées (31° N, 74° E).
On arrondira donnera un résultat arrondi au \( km \).
On arrondira donnera un résultat arrondi au \( km \).
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Nos exercices sont conformes aux programmes de l'Éducation Nationale de la 6e à la Terminale. Grâce à Kwyk, les élèves s'entraînent sur du calcul mental, des exercices d'arithmétique et de géométrie, des problèmes et des exercices d'application, des exercices d'algorithmique et de python, des annales du brevet des collèges et du baccalauréat. Nos exercices sont proposés sous forme de réponse libre et/ou de QCM.
Afin d'assurer un entraînement efficace et pertinent aux élèves, chaque exercice est généré avec des valeurs aléatoires. Les élèves peuvent s'entraîner grâce aux devoirs donnés sur Kwyk par leurs professeurs et aux devoirs générés par notre outil utilisant l'IA mais aussi grâce aux différents modules de travail en autonomie mis à disposition sur leur espace personnel. Pour les niveaux du collège, les élèves ont également accès à des cours constitués d'une partie théorique et d'une partie pratique.
Avec Kwyk, vous mettez toutes les chances du côté des élèves pour que les différents théorèmes, propriétés et définitions n'aient plus aucun secret pour eux.
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