Throughout our lives, we constantly have to calculate the volume of various geometric shapes. So, 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 production. When completing the school curriculum, the "Geometry" section details the methods for calculating the volumes of various geometric shapes. But what to do for those who have long forgotten about schoolwork? This article will help you remember everything.
First, we’ll show you how to calculate the volume of regular geometric bodies. These include a pyramid, a rectangular box, a cone, a cylinder, a box and a sphere.
A pyramid is a polyhedron, the base of which is a polygon. All other faces are triangles having one common vertex. In order to determine the volume of such a geometric body, it is necessary to know or calculate the base area and height. The volume of the pyramid will correspond to the third part of the product of the height and base area of this figure. In the form of a formula, it will look like this:
V = 1/3 • S • h
The next one on our list is the box. How to calculate the volume of this figure? A parallelepiped is a prism with a parallelogram at its base. If all four faces, called side faces, are rectangles, then such a box is called straight. If all six sides are rectangles, then this is a rectangular box. The volume of such a figure corresponds to the product of two quantities: the base area and the height of the figure. In the form of a formula, this can be written as follows:
V = S • h
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 is the width, b is the length, and h is the height of the figure.
The cone, which is obtained due to the rotation of a triangle having a right angle around one of its legs, also belongs to simple figures. 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.
V = 1/3 • S • h
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.
Now consider how to calculate the volume of a cylinder? Recall what this figure represents. A cylinder is a shape that results from the rotation of a rectangle around one of its sides. Its volume corresponds to the product of the height and the 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? There is the following formula for this:
V = 4/3 • 3.14 • r³
As you can see from the above, to calculate the volume of any geometric body is not difficult, knowing the formula. If some value in the formula is unknown, it is necessary to calculate it, already considering the necessary flat figure.
In addition, it should be noted that all values used 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 figures, there are more complex figures: a truncated pyramid, a hollow cylinder, and others. There will already be other formulas. So, for example, the volume of a hollow cylinder will be equal to the difference between the volumes of a larger cylinder and a smaller one. There is nothing complicated in calculating this data. It is simply necessary to imagine this body and the fragment that is cut from it. You see, the solution to the question will come by itself. And do not despair if something does not work out, just carefully read this article.