The rectangular parallelepiped: how to calculate its volume, how to draw it, the formulas and an example explained step by step.
In geometry, the rectangular parallelepiped is a particular type of polyhedron , which has 6 flat polygonal faces where each face is a parallelogram, called a hexahedron. The parallelepiped is a solid that has the shape of a box. It is made up of 4 rectangles and 2 squares , one for each of its faces. Together with the cube, the rectangular parallelepiped is one of the easiest solids to understand, which is why it is studied in the early stages of school . In this guide, we will see in detail how to calculate the volume of a rectangular parallelepiped.
Draw a rectangular parallelepiped
When studying Euclidean geometry , especially in the case of solids (three-dimensional bodies with faces, edges, vertices and angles) the first thing to do is to arm yourself with a pencil and ruler and draw . In our case, having a rectangular parallelepiped in front of our eyes, we will be able to more easily understand the formulas that concern it and their application. Let’s see how to trace it on paper.
- Draw a rectangle;
- draw a second rectangle identical to the first but positioned above and slightly to the left of the first;
- join the two rectangles at their vertices, drawing connecting lines between the upper left corner of the first rectangle and the upper left corner of the second;
- repeat for all corners.
That’s it: admire your first rectangular parallelepiped.
Volume: first formula
By definition, the volume of a solid figure consists of the space or quantity of air that it encloses. The unit of volume is measured in cm³ (cubic centimeters). To calculate the volume of a solid of this type, you can use two formulas : the first requires that the volume is the product of its dimensions, therefore it is obtained by multiplying its length, width and height. This results in the formula: V= (a)(b)(c) .
Volume: second formula
The second formula that we can use to obtain the volume of a rectangular parallelepiped is: V=A (h) . The volume is obtained, in this case, by multiplying the base area and the measure of the relative height. Let’s try to understand better by going into specifics.
Since the base of the parallelepiped is a rectangle, the multiplication “(a)(b)” represents the base area. For this reason, the volume can be written as ” V= A (h) “, or as a multiplication between “A” (base area) and “h” (measurement of the relative height).
Having assimilated the formula to obtain the volume, we can consequently also obtain the inverse formulas for calculating the base area and the height, that is respectively ” A= V/h” and “h= V/A “.
Example
Now let’s take an example. Suppose we need to calculate the volume of a parallelepiped whose dimensions measure 3, 4 and 12 cm, and therefore a=3 cm, b=4 cm and c=12 cm.
For the first formula written, ” V=(a)(b)(c) “, we will have that V=(3)(4)(12) , and the result of our calculation will therefore be 144 cm³.
Let’s now try to apply the second formula, V=A (h) . First we have to find the area of the rectangle, which is the base of the parallelepiped, by multiplying (a)(b), and then (3)(4). So we can write the formula as V=(3)(4)(h) and, since h=c and the value of c=12 cm , we can write V=(3)(4)(12) .
Even in this way, by doing the right calculations, we will obtain that the volume of our rectangular parallelepiped is equal to 144 cm³. The volume of a parallelepiped, therefore, whose dimensions measure 3, 4 and 12 cm, is 144 cm³.
