All planets of the solar system have the sphere form. Besides, also many objects created by the person including details of technical devices have the form, spherical or close to that. The sphere, as well as any body of rotation, has an axis which coincides with diameter. However it not only important property of a sphere. Below the main properties of this geometrical figure and a way of finding of its area are considered.
Instruction
1. If to take a semicircle or a circle and to turn it round its pivot-center, the body called a sphere will turn out. In other words, a sphere is called the body limited to the sphere. The sphere represents a sphere cover, and its section is the circle. It differs from a sphere in what is hollow. The axis both at a sphere, and at the sphere coincides with diameter and passes through the center. Radius of a sphere is called the piece laid from its center to any external point. Contrary to the sphere, sections of a sphere represent circles. The form close to spherical, the majority of planets and celestial bodies has. In different points of a sphere are available identical in a form, but unequal in size, so-called sections are circles of the different area.
2. A sphere and the sphere - interchangeable bodies, unlike a cone in spite of the fact that the cone is also a rotation body. Spherical surfaces always in the section form a circle no matter how it rotates - across or down. The conic surface turns out only at rotation of a triangle along its axis perpendicular to the basis. Therefore the cone, unlike a sphere, is also not considered an interchangeable body of rotation.
3. The biggest of possible circles turns out at sphere section the plane passing through center O. All circles which pass through the center Oh, are crossed among themselves in one diameter. Radius is always equal to a half of diameter. Through two points of A and B which are located in any place of a surface of a sphere there can pass the infinite number of circles or circles. For this reason through poles of Earth the unlimited number of meridians can be carried out.
4. When finding the area of a sphere, first of all, the area of a spherical surface is considered. The area of a sphere, to be exact, of the sphere forming its surface can be calculated on the basis of the area of a circle with the same radius of R. As the area of a circle is the work of a semi-circle on radius, it can be calculated as follows: S =? R^2Так as through the center of a sphere there pass four main big circles, respectively the area of a sphere (sphere) is equal: S = 4? R^2
5. This formula can be useful in case either diameter, or radius of a sphere or the sphere is known. However, these parameters are specified as conditions not in all geometrical tasks. There are also such tasks in which the sphere is entered in a cylinder. In this case, it is necessary to use Archimedes's theorem which essence is that the surface area of a sphere is one and a half times less than a full surface of a cylinder: S = 2/3 S tsit. where S tsit. - the area of a full surface of a cylinder.