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 Oberfla¨cheinGerman.
The formulas are organized by shape:
- 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.
- 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.
- 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.
- 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.
- Zylinder Cylinder:
Volume: V = πr²·h
Definition: A cylinder is a three-dimensional shape with two circular bases connected by a curved surface.
- Kegel Cone:
Volume: V = 1/3πr²·h
Surface Area: O = πr² + πrs
Vocabulary: In a cone, 's' represents the slant height.
- 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?
