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Cube, general

A cube has six congruent squares as boundary surfaces - https://domyhomework.club/ , which lie parallel to each other in pairs. To calculate the surface area and the volume, it is therefore sufficient, for example, to specify the length of the body edge of the cube.

A cube is a special cuboid and belongs to the four-sided prisms with edges at right angles to each other. A cube has six congruent squares as boundary surfaces, which are parallel to each other in pairs.

In a cube, all twelve diagonals of the surface and all four diagonals of the space are of equal length - https://domyhomework.club/math-homework/ . To calculate the surface area s and the volume s, it is sufficient, for example, to specify the length of the body edge of the cube.

AO, cube=6a^2

V=a^3

Example:

A cube-shaped box made of wood has an edge length of 80 cm - https://domyhomework.club/statistic-homework/ . How many square metres of wood are needed to make a box and what is its volume?

Wanted: AO in m^2; V in m^3

Given: a = 80 cm = 0.8 m

Solution:

AO=6a^2

V=a^3

AO=6⋅(0.8 m)^2

V=(0.8 m)^3

AO≈3.8 m^2

V≈0.5 m^3

Answer: 3.8 m^2 of wood are needed at least for one crate. The crate has a volume of approx. 0.5 m^3.

Normal images

The images in a vertical parallel projection are called normal images. The plan and elevation of a body are special normal images. Usually a special position of the body is chosen in which as many boundary surfaces as possible are parallel to one of the image planes. Since many edges are then perpendicular to an image plane and are therefore depicted as points, the images are often not very descriptive. For example, the elevation and ground plan of a cube are each a square.

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