In terms of geometry a pyramid is a geometric figure that is formed by means of connection between a specific point (this point is usually called the «apex») and a polygonal base. The specificity of this figure is that every edge of the base together with the point on the top of the figure from a triangle. The triangle that is created by means of apex and the base of the pyramid is usually called as a lateral face. Another specificity of this kind of geometric figure is that all of them without exceptions are self-dual, which means that the dual of this figure has absolutely the same connectivity between all the parts of the figure, including the faces, all the edges and the vertices. In other words, all sides of the figure are completely identical. There are different kinds of pyramids, each of which is characterized by certain specificities and has its own properties. In order to be able to find the volume of a pyramid it is important to not only know the formula of the volume of a pyramid, but also to have essential theoretical background allowing to understand the basics of geometry and pyramids, as well. In this article, you will find the needed information and learn how to find the volume of a pyramid, depending on the dimensions that are provided in your assignment.
First of all, before you proceed to calculating the volume of a pyramid it is necessary to know and understand the types of pyramids, how to distinguish one type of a pyramid from another, what determines that or another type of pyramid and so on. Therefore, take a look at the following types of this geometric figure:
- A right pyramid. This type of geometric figure is characterized by the apex that is located precisely above the centroid of the ground (base) of the pyramid. In terms of mathematics, by centroid, one should mean the geometric center of the figure that indicates the central position of all the points of the figure.
- An oblique pyramid. This type of geometric figure is non-right, in contrast to the one that was described in the previous statement. This means that the geometric center (the centroid) of the figure doesn't indicate the position of the apex.
- A regular pyramid. This is the third and the last type of a pyramid that is characterized by a regular polygon ground (base). When talking of the regular polygon, one should mean the plane figure with a constant chain of straight segments in the form of lines, where all the angles have absolutely the same dimensions. As a rule, this type of pyramid is also the right one, since the centroid of the figure determines the position of the apex.
When you have a geometric assignment where you have to calculate the volume of a pyramid, you need to read the assignment carefully and figure out whether it says something concerning the type of the pyramid. In case if there is no information providing the type of the figure, you should consider the given pyramid to be the regular square pyramid. Below in the article, you will learn how to deal with calculating the volume of a pyramid.
Measuring the volume of a pyramid
In order to calculate the volume of a pyramid the most important thing you have to do is to determine the product of the geometry figure base and the height of the figure. After that, you will have to multiply the received number by 1/3. Having said that, such methodology of measuring the volume of a pyramid may very significantly, depending on the type of the pyramid, whether it is a geometric figure with rectangular base or with triangular base. In any case, for dealing with measuring the volume of a pyramid, you need to undertake a number of steps. If the pyramid you are dealing with has a rectangular base, the steps will be the following:
- At first, find out the dimensions of the base of the figure. You need to know the numbers indicating the length and the base of the pyramid. In case if you are dealing with the square base, you will have to do the same thing, although keep in mind that both the length and the width of the base that has a square form will be absolutely equal. Once you got these numbers found, you need to write them down.
- The second step will be doing operations with the dimensions that you have already determined. You will have to multiply the width of the figure and its length in order to find out the area of the pyramid's base. For example, if the length of the figure is 5 cm and the width is 7 cm, the are will be 35 cm (5 x 7 = 35).
- The next thing you should do is multiplying the area of the pyramid's base by the number indicating the height of the pyramid. For example, if the height is 8 cm and the area is 35 cm, the result will be 280 cm.
- Now you need to divide the result received due to the previous operation by three. Thus, you will find the volume of a pyramid. Keep in mind that in case if you are dealing with a three-dimensional space, you will have to state the answer that you will get after undertaking this step in cubic units.
These were steps to undertake if the pyramid provided in the geometric assignment has a rectangular base. But if the given pyramid has a triangle base, the steps you need to undertake will be the following:
- First of all, you need to determine the length of the pyramid's base and its width. Keep in mind that in this type of a pyramid the length and the base of the figure's base have to be perpendicular in regard to each other, otherwise this method of calculating the volume of a pyramid will not work correctly. These two parts of the pyramid can be considered the height and the base of the triangle.
- Remember that if you see that the width of the figure and its length are not perpendicular, you have to look for other methods of calculating the triangle's area.
- Your next step is going to be calculating the area of the geometric figure's base. In order to deal with calculating of the pyramids base, you need to do some operations with the height and the base of the triangle according to the following formula: a = ½ (b)x(h), where “a” will indicate the needed are.
- The next thing you need to do is multiplying the area of the pyramid's base that you have found during the previous step by the height of the geometric figure.
- The final step of your calculating process will be dividing the received result by three. As a matter of fact, the number will determine the volume of a pyramid and this is going to be the answer to the question of your assignment.
Now that you are aware of the easiest and most common methods of calculating the volume of a pyramid, it would be good to learn some interesting information about the pyramids themselves, their own history and their role in the history of humanity. All this information is provided below in the article, so keep reading attentively.
Interesting facts about pyramids
The word «pyramid» has originated from the Greek language long time ago. People in different parts of the world were studying pyramids since the beginning of times. The shape of a pyramid is very convenient if you want to save the building resources, because most of weight of the figure is closer to the ground, and the higher the figure is the less material is needed to build it. Such thoughts played a significant role in early civilization's way of life, considering that a great number of buildings that you can see even today were made up in the form of a pyramid. In addition, the research has shown that building of monumental structures in the form of a pyramid requires much less human force and efforts to be spent.
Far and wide across the world, different buildings in a form of pyramids have been built with various purposes. During hundreds and even thousands of years, the biggest and the strongest monumental constructions on the planet were pyramids. The majority of these structures have been built in Egypt, although there are also huge pyramids in other countries, as well. The most famous pyramids, however, are those located in Egypt. People all over the world come to see those phenomenal monumental structures, some of which are considered to be on the top of the list of the biggest constructions of the world. The age of pyramids demonstrates how long may serve buildings of such form.
Pyramids around the world
As we have already said, people began to build monumental structures in the form of pyramids thousands of years ago. Pyramids can be found on all the continents and the majority of them are so old that it is difficult to imagine how people of ancient civilizations could manage to build such huge structures. Look where you can find pyramids the age of which is more than a thousand of years.
- As a matter of fact, the earliest buildings in the form of pyramid were build by Mesopotamians. These buildings are called «ziggurats». At times when these pyramids were created, people painted them in bright colors that looked similar to gold and bronze. The purpose of creating such buildings was religious: Mesopotamians believed that gods lived in those pyramids.
- In fact, Egyptian pyramids are considered to be the most popular and famous in the world. You can hardly find a person who has never heard of these pyramids. Some of the pyramids in Egypt belong to the biggest buildings in the world, even including contemporary structures. The age of some pyramids created in that part of the world is more than three thousand years.
- In this part of the world, constructions in the form of pyramids were created with the purpose of serving the kings and queens. These pyramids are different from the Egyptian because they were created at a steeper angle and they were higher than the Egyptians.
- In this country, the most famous pyramids are the Nsude Figures. There are three of them and the research has shown that all of them were build by means of mud, which was not beneficial to the quality of the constructions.
- The pyramids in this country have a lot of mysteriosity and the purpose of their building is not really recognized yet. Inside the monumental structures and on the territory near them you can't find any graves or remains. But instead, they are different from the pyramids in other countries because the rooms inside of them are all made to be locked not from the outside, but from the inside. One of the versions of what these constructions could serve for is to be watchtowers. However, some researchers argue that these pyramids were created to serve as shrines for soldiers of that historical period, although this version doesn't explain the lock on the inside of the constructions.
- Not everyone knows, but there are also pyramids in Spain, which were built from such material as lava stone. Unfortunately, only a few of pyramids on the territory of Spain managed to survive, since they were made from cheap building material.
- The monumental constructions in India have always served for different religious purposes. And even today their meaning and functions remain the same. The Indian pyramids are almost as huge as Egyptian, although they are not so old.
- Roman Empire. There were two pyramids built and only one still exists. Unfortunately, the second pyramid was destroyed during the time of wars in the fifteenth century.
As you can see, there are a lot of interesting facts about pyramids. They belong to the list of the most mysterious constructions in the history of the world, and worth to be learn about.
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