Pour aller plus loin (Ancien programme) - 5e
Géométrie dans l'espace
Exercice 1 : Lire les coordonnées géographiques d'une ville sur terre à partir des angles
Sur le schéma ci-dessous, le point D symbolise la ville de Rāmgundam (Inde).
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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 Rāmgundam
Sachant que \( \widehat{DCN} = 71 ° \), \( \widehat{ABD} = 79 ° \), \( \widehat{ECD} = 19 ° \) et \( \widehat{SCE} = 90 ° \), donner les coordonnées géographique de la ville de Rāmgundam (Inde).
Par exemple:
Par exemple:
- Pour la ville de Bordj-Bou-Arreridj (Algérie) on donnera une réponse de la forme \(\left(36° N; 5° E\right)\)
- Pour la ville de Chiclayo (Pérou) on donnera une réponse de la forme \(\left(7° S; 80° O\right)\)
Exercice 2 : Calculer la longueur de l'équateur ou d'un méridien à partir du rayon/diamètre de la planète
Sur une planète de diamètre \( 5\:100\:\text{km} \), 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 3 : 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 Hachinohe (Japon).
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"PlaneSurface", "path": "Circle_52"}, "Circle_52": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 7.445927106677217, "y": 7.445927106677217}}}]}, "PlaneSurface_55": {"position": {"x": 0.0, "y": 39.39231012048832, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 8487415, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_54"}, "Circle_54": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 7.445927106677217, "y": 7.445927106677217}}}]}, "Point3D_D": {"type": "Point", "position": {"x": 23.4729635533386, "y": 25.71150438746157, "z": 19.696155060244166}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": 23.4729635533386, "y": 25.71150438746157, "z": 19.696155060244166}, "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°
- Méridiens (espacés de 20°)
- Équateur 0°
- Parallèles (espacés de 20°)
- N : Pôle nord
- S : Pôle sud
- D : Ville de Hachinohe
Donner la longitude de la ville de Hachinohe (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 4 : Calcul du volume d'une boule
Soit une boule de \(18 cm\) de rayon.
Calculer son volume.On donnera le résultat exact.
Exercice 5 : Lire les coordonnées d'un point dans un plan 3D
Dans le repère ci-dessous, donner les coordonnées du point M sous la forme \((x ; y ; z)\).
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