The volume of the parallelepiped

For the first time, a person encounters calculating the volume of a parallelepiped at school. To begin with, let’s also remember what describes each word from the designated concept. Volume is a quantitative characteristic of the space occupied by a body or substance. A parallelepiped (from ancient Greek – “parallel plane”) is a prism (polyhedron) with four corners, which is based on a parallelogram (quadrilateral); in other words, it is a polyhedron with six faces (i.e. a hexagon), where each of them is a parallelogram.

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The volume of a rectangular parallelepiped

Length of the parallelepiped edge a
Length of the parallelepiped edge b
Length of the parallelepiped edge c

Types of parallelepipeds

• rectangular– where all the faces are rectangles;
• straight– which has four side faces – rectangles;
• inclined– whose side faces are not perpendicular to the bases;
• rhombohedron (from the word “rhombus”) – whose faces are equal rhombuses;
• a cube (aka a regular polyhedron) – whose faces are squares (i.e. regular quadrilaterals).

Let’s focus here on a rectangular kind of parallelepiped, i.e. a cuboid. In other words, it is a polyhedron (polyhedron) with six faces, where each of them is a rectangle (i.e. a quadrilateral, each corner of which is a straight line).

In his life, a person meets cuboids every day: an ordinary classroom at school, a thick encyclopedia or any other book, a building brick, a matchbox, a wardrobe, a computer system unit, etc. there is a rectangular parallelepiped.

Often, in the process of working with this type of “parallel plane”, it is necessary to calculate the volume of a rectangular parallelepiped.

This is done according to the following formula: V=a×b×c ,

where a, b and c are its dimensions, i.e. length, width and height respectively.

Measurements are often referred to as the lengths of three edges that belong to one vertex. Note also that often the height is indicated by the letter h instead of c.

It turns out the following: THE PRODUCT OF the known values OF THE LENGTH, WIDTH AND HEIGHT OF THIS PARALLELEPIPED IS ITS VOLUME.

The volume of a straight parallelepiped, for example, can be found in a slightly different way, knowing only the size of the base area and height.

Here the formula for calculations is as follows: V=Sоof the base×h ,

where S of the base is actually the area of the base,

h– height of the parallelepiped.

If, on the contrary, it is required to find the area of the base, while knowing the volume and height of the parallelepiped, use a slightly different formula: S of the base=V/h