Geometric Formulas for 3D Shapes

This page presents a comprehensive collection of formulas for calculating the volume and surface area of various three-dimensional shapes. These formulas are essential for students studying geometry and working with geometrische Körper.

Vocabulary: V represents volume, while O represents surface area (Oberfläche in German).

The formulas are organized by shape:

1. Würfel (Cube):
   • Volume: V = a³
   • Surface Area: O = 6a²

Definition: A cube is a three-dimensional shape with six equal square faces, where 'a' represents the length of one edge.

2. Quader (Cuboid):
   • Volume: V = abc
   • Surface Area: O = 2ab + 2bc + 2ac

Example: In a cuboid, 'a', 'b', and 'c' represent the length, width, and height respectively.

3. Kugel (Sphere):
   • Volume: V = 4/3πr³
   • Surface Area: O = 4πr²

Highlight: The sphere is unique among these shapes as it has no edges or vertices.

4. Prisma (Prism):
   • Volume: V = G·h
   • Surface Area: O = 2G + M

Vocabulary: G represents the area of the base, h is the height, and M is the lateral surface area.

5. Zylinder (Cylinder):
   • Volume: V = πr²·h

Definition: A cylinder is a three-dimensional shape with two circular bases connected by a curved surface.

6. Kegel (Cone):
   • Volume: V = 1/3πr²·h
   • Surface Area: O = πr² + πrs

Vocabulary: In a cone, 's' represents the slant height.

7. Pyramide (Pyramid):
   • Volume: V = 1/3G·h or 1/3a²·h
   • Surface Area: O = G + M

Example: For a square-based pyramid, 'a' would be the length of one side of the base.

This collection of formulas serves as an excellent Formelsammlung Geometrie Körper PDF for students learning about Wie berechnet man Körper in der Mathematik? It provides a quick reference for calculating both volume and surface area of common geometric shapes, answering questions like Wie berechnet man den Flächeninhalt eines Körpers? and Wie lautet die Formel des Volumens?