In the field of geometry, a body is an element that has three dimensions: height, width and length. According to their characteristics, it is possible to distinguish between different types of geometric bodies.
Round bodies have one or more curved surfaces or faces. This allows them to be differentiated from flat bodies or polyhedrons, composed entirely of flat faces.
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Cones are examples of round bodies. It is a solid of revolution that is formed from the rotation of a right triangle around a leg. Let’s see below each of the parts of the cone with a brief definition of each:
* axis : this is the leg around which the right triangle must rotate to form the cone;
* base : is the circle that arises as a result of the rotational movement of the other leg. This leg is also considered the radius of the cone, that is, half the diameter;
* generatrix : this is the name of the hypotenuse of the right triangle, which produces the lateral zone of the cone, which is known as the mantle ;
* cusp : it is the vertex located in the upper part, in what we could call “the tip” of the cone.
The missing element in the above list is the height of the cone, since its definition admits two possibilities that must be taken care of separately. If this property of the round body is equivalent in magnitude to the extension of the axis, that is to say that it forms a line perpendicular to the base uniting its center with the apex, then we are faced with a right cone.
Although this is the shape we associate with the cone in everyday speech, there is also another variety: the oblique cones. These round bodies have a height that does not coincide with the extension of the axis, since it does not form a perpendicular line with the base, but has a certain inclination.
In a case like this, if we want to know the height of the cone, we must project the apex onto the plane on which the base is located, drawing a perpendicular line, and then measure the distance between both points.
Thinking about the theoretical or imaginary steps that we must follow to build a cone, which in some cases can be found spontaneously in elements of nature, is necessary to access the series of calculations related to the measurement of its dimensions and properties.
By decomposing a cone into an infinite series of identical right triangles, we can take advantage of the equations of these simpler geometric shapes to calculate the height of the main structure and the diameter of the circumference that acts as the base of the round body, since the smaller leg of the triangle will be equivalent to its radius, which we must multiply by two.
Traffic cones used to order traffic or warn drivers are round bodies. These cones are usually made of plastic and are brightly colored to attract attention.
Cylinders are also round bodies. In this case, the object develops from the parallel displacement of the generatrix (straight) by the directrix (flat curve). When the generatrix is perpendicular to a directrix that is in the shape of a circle, a right circular cylinder is formed. Toilet paper, to cite one case, is rolled up in a cardboard cylinder.
Spheres also appear among round bodies, which are surfaces of revolution made up of points that are equidistant from a center. A soccer ball (ball) is a sphere. It should be noted that the body that delimits a sphere is also known as a ball.