Parallelepipeds are rectangular solids with two parallel sides and two sets of perpendicular sides. The volume of a parallelepiped is the volume of the shape it would be if it were rotated, translated, and stacked with an identical shape.
Parallelepipeds can be described by the adjacent edges that compose them. An edge is a line segment joining two vertices of the parallelepiped. A vertex is a corner point of the parallelepiped.
There are three types of parallelepipeds: 1) those with all horizontal edges, 2) those with all vertical edges, and 3) those with one set of horizontal edges and one set of vertical edges. This article will discuss how to find the volume of these three types of parallelepipeds.
Calculate the volume of each individual face
Now that you have the dimensions of all of the edges, you can calculate the volume of each individual face. The volume of a single face is equal to the length times the width times the height.
So, Vface= PvqPrPs where P is the thickness of the material and v is the volume of one side. This formula is for a cube, so make sure to adjust it for your shape!
To find the total volume, add up all of the individual faces and divide by three (since there are three dimensions). The total volume will be in cubic units, such as cubic meters or cubic centimeters.
Remember: You calculated the area first, so you already have that information! Calculate the volume next to find out how much material your shape is made out of.
Use formulas for calculating the volume of a parallelepiped
Now that you can calculate the area of the parallelogram shaped by the adjacent edges, you can use that area as the base to find the volume of the parallelepiped.
The volume of a parallelepiped is calculated by adding all of its bases and multiplying that sum by the perpendicular height. The height is always represented by one of the sides of the solid.
Example: Find the volume of a parallelepiped with rectangular bases whose length is 3 units and whose width is 4 units, where Pq, Pr, and Ps are perpendicular to each other.
To solve this problem, first find the area of each base using the formula for a rectangle: A=lw. Then, add these areas together to get the total base area.
Next, find the height using Pq=Pr=Ps=x. Then, solve for y in order to find the perpendicular height using y=2x-y=2(3)-y=6-y=0.
Compile your results to find the total volume
Once you have the individual volumes for each of the parallelepipeds, you can find the total volume of all of them. You can do this by adding, multiplying, or dividing them, depending on what is easier for you to do.
To add them, add up all of the base lengths and all of the heights for each parallelepiped and then add these numbers together. This will give you the total height of all of the parallelepipeds. Then, take the total area of the bases and multiply that by this height to get the total volume.
To multiply them, take the product of all of the bases for each parallelepiped and then multiply that by the height of each one. Add all of these numbers together to get the total volume.
To divide them, take the division between any two volumes and then divide that by the last volume to get the total volume.
Check your work for accuracy
Once you have the total number of units in the parallelepiped, and you know how to calculate the area of each side, your next task is to calculate the volume of the parallelepiped.
Once again, in order to calculate the volume of the parallelepiped, you must first find the volume of each side, and then add these together. You can do this by using A=pr2h, where A is area, p is width of side, r is radius of circle used to produce side, and h is height.
Once you have calculated the individual sides’ volumes, then you can find the total volume of the parallelepiped by using V=Ah. Where V is volume, A is area, and h is height.
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