The volume of the cone

components cone

To find the volume of a cone, you need to know what it is.The base of the geometric body and the top are the main generators of the geometric figure.

straight line joining the top of the cone with the base boundary, called generators.

images (conical) or conical surface is a union of all generators.Height figure is a line which connects the top and bottom of the cone at right angles to the base.The line that connects the top and center of the base, called the axis.Also be aware that the angle between the two opposing components called aperture angle.

Types

For such shapes as a cone, the amount of mathematics is calculated using different formulas, which vary depending on the species.When it comes to the cone, most imagine the circle at the bottom and a sharp peak.But this is a misconception people have forgotten that the course curriculum.Kind cone when its base forms a circle, called the circular.If the base of the cone is a polygon, then it will be a pyramid.If the basis

is an ellipse, parabola or hyperbole, such a figure is called, respectively, elliptical, hyperbolic and parabolic cone.The last two cases are of infinite volume of the cone.

Varieties of the geometric shape can be divided into the following types: right and wrong cone.The second case assumes that the top with the geometric center of the base is connected to a line perpendicular to the base, which is a circle or a regular (equilateral) polygon.For example, perpendicular to the line connecting the center of the circle or the point of intersection of the diagonals of the square from the top.If the vertex is offset with respect to the symmetric center of the base of the geometric figure, it is designated as a scythe.

In addition, there is a truncated cone (truncated pyramid) that, based on the definition of school geometry course, not a single geometric figure, but is only part of a cone (the pyramid).In other words, a plane that is parallel to the plane of the base of the cone cuts a smaller cone, and the remaining part is a truncated cone.However, another definition of the curriculum quite differently interprets the concept of a truncated cone as a distinct geometric shape (in the case of a circular) body obrazovanneo rotation around a rectangular trapezoid side, which forms a trapezoid with bases angles.

volume of a cone and a truncated cone

Greek scientists have long ago brought the formula to help calculate precisely the amount of both the cone and the truncated part.

order to calculate the volume of the cone, we need to multiply the area of ​​the base and the height of the cone, and then the resulting product divided by three.Privately which we work, and will be an area of ​​the cone.The same formula is used for calculating the volume of a pyramid, as a special case of the cone.On paper, the formula is as follows: O = UCR / 3, where C - the area of ​​the base B - height.

For geometrical figure "truncated cone" is calculated according to the volume of a more complex formula, which, however, is also not something transcendent and complex.The amount of base radius squared, summed with the product of the radius of the base.The resulting number is multiplied by a constant π (3,14) and then multiplied by the height.The result of the product is divided by 3. The formula for calculating the amount of paper will be as follows: D = VHπH (R1HR1 + R1HR2 R2HR2 +) / 3.In this formula, V - height of the truncated cone, P1 - the radius of the lower base, P2 - the radius of the upper base, π - constant number (3.14).