Throughout our lives constantly have tocalculate the volume of those or other geometric shapes. For example, during construction it is necessary to correctly calculate the volume of trenches and excavations. In addition, this value is determined by almost all designers in industry. During the passage of the school curriculum in the "Geometry" section, the methods of calculating the volumes of various geometric shapes are described in detail. But what about those who have long forgotten about schoolwork? This article will help you remember everything.
First we will explain how to calculate the volume of regular geometric bodies. These include a pyramid, a rectangular parallelepiped, a cone, a cylinder, a parallelepiped and a sphere.
The pyramid is a polyhedron,the base of which is a polygon. All other faces are triangles with one common vertex. In order to determine the volume of such a geometric body, it is necessary to know or calculate the area of the base and height. The volume of the pyramid will correspond to the third part of the product of the height and area of the base of this figure. In the form of a formula, it will look like this:
B = 1/3 • C • x
Next on our list is a parallelepiped.How to calculate the volume of this figure? A parallelepiped is a prism with a parallelogram at its base. If all four faces, called lateral, are rectangles, then such a parallelepiped is called straight. If all six sides are rectangles, then this is a rectangular parallelepiped. The volume of such a figure corresponds to the product of two quantities: the area of the base and the height of the figure. In the form of a formula, this can be written as:
B = C • x
As for the volume of a rectangular parallelepiped, it is calculated as the product of its length, width and height.
V = a • b • h, where
a - width, b - length and h - the height of the figure.
К простым фигурам относится и конус, который is obtained due to the rotation of a triangle having a right angle around one of its legs. How to calculate the volume of the cone? Quite simply, it corresponds to the third part of the product of the base area and height.
B = 1/3 • C • x
In addition, the volume of the cone can be calculated by the formula:
V = 1/3 • n • r² • h, where
n = 3.141592,
r is the radius of the circle lying at the base.
А теперь рассмотрим, как рассчитать объем top hat? Recall what is this figure. A cylinder is a figure that is obtained by rotating a rectangle around one of its sides. Its volume corresponds to the product of height and area of the base. The formula is written as follows:
V = n • R² • h.
A sphere is a closed figure in which all its forming points are at the same distance from the center. How to calculate the volume of such a body? For this there is the following formula:
V = 4/3 • 3.14 • r³
As you can see from the above, calculate the volumeany geometric body will not be difficult, knowing the formula. If any value in the formula is unknown, you need to calculate it, already considering the necessary flat figure.
In addition, it should be noted that all valuesused in the same formula should be presented in equal units. For example, if the radius is expressed in meters, then the height must also be expressed in meters, otherwise the answer will be false.
In addition to the described geometric shapes there areand more complex shapes: a truncated pyramid, a hollow cylinder and others. There will already be other formulas. For example, the volume of a hollow cylinder will be equal to the difference in volumes of a larger cylinder and a smaller one. When calculating this data there is nothing difficult. You just need to submit this body and the fragment that is cut from it. You'll see, the issue will come by itself. And no need to despair, if something does not work out to solve, just carefully read this article.
