Solides

Pour aller plus loin (Ancien programme) - Mathématiques 3e

Exercice 1 : Calcul de l'aire d'une sphère

Soit une sphère de \( 3 cm \) de rayon.

Calculer son aire.
On donnera un résultat exact.

Exercice 2 : 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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"Label_for_Point3D_93": {"type": "Label", "position": {"x": 0.0, "y": 0.0, "z": 0.0}, "text": "0", "position_offset": {"x": 0.0, "y": -3.52, "z": 0.0}}, "Segment3D_94": {"type": "Segment", "pt1": {"x": 0.0, "y": 0.0, "z": 0.0}, "pt2": {"x": 0.0, "y": 1.2, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}}, "Segment3D_95": {"type": "Segment", "pt1": {"x": 0.0, "y": 0.0, "z": 0.0}, "pt2": {"x": 1.2, "y": 0.0, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}}, "Segment3D_96": {"type": "Segment", "pt1": {"x": 0.0, "y": 0.0, "z": 0.0}, "pt2": {"x": 0.0, "y": 0.0, "z": 1.2}, "point_render": {"visible": false}, "label_render": {"visible": false}}, "Point3D_97": {"type": "Point", "position": {"x": 24.0, "y": 18.0, "z": 36.0}, "point_render": {"color": 204}, "label_render": {"color": 204}}, "Label_for_Point3D_97": {"type": "Label", "position": {"x": 24.0, "y": 18.0, "z": 36.0}, "text": "M", "position_offset": {"x": 0.0, "y": 3.52, 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"Segment", "pt1": {"x": 24.0, "y": 18.0, "z": 36.0}, "pt2": {"x": 0.0, "y": 18.0, "z": 36.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"color": 204, "dashed": true}}}}

Exercice 3 : Calcul d'un rayon à partir de l'aire d'une sphère

Soit une sphère d'aire \(169\:cm^{2}\). Calculer son rayon.

On donnera le résultat sous la forme d'une valeur exacte avec \( \sqrt{\pi } \).

Exercice 4 : Calcul de l'aire d'une sphère

Soit une sphère de \( 5 cm \) de rayon.

Calculer son aire.
On donnera un 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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