When people are asked the question, what is the difference between spheres and a sphere, many simply shrug their shoulders, thinking that in fact they are one and the same (analogy with a circle and a circle). Indeed, do all of us know geometry well from the school curriculum and can immediately answer this question? The sphere has some differences from the sphere that need to be known not only for schoolchildren in order to get a good grade for their demonstrated knowledge, but also for many other people, for example, whose work is directly related to drawings.
Ball - the collection of all points in space. All these points are located from the center of the geometric body at a distance that is not more than a given one. This distance itself is called the radius. A ball, as a geometric body, is formed as follows: a semicircle rotates near its diameter. As for the sphere, this is the surface of the ball (for example, a closed ball includes it, an open one does not). Calculating the area or volume of a ball are whole geometric formulas that are very complex, despite the seeming simplicity of the geometric figure itself.
The sphere, as noted above, is the surface of the ball, its shell. All points in space are equidistant from the center of the sphere. As for the radius of a geometric body, it is called any segment, one point of which is directly the center of the sphere, and the other can be located at any point on the surface. We can say that a sphere is a shell of a sphere without any content (more specific examples will be given below). Just like a ball, a sphere is a body of revolution. By the way, many also wonder how a circle and a circle differ from a sphere and a ball. Everything is simple here: in the first case, these are figures on a plane, in the second - in space.
It has already been said that the sphere is the surface of the ball, which already makes it possible to speak about one significant feature of the difference. The difference between the two geometric bodies is observed in some other aspects:
- All points of the ball are at the same distance from the center, while the body is limited by a surface (a sphere that is empty inside). In other words, the sphere is hollow. Usually, for ease of understanding, they give a simple example with a balloon and a billiard ball. Both of these objects are called balls, but in the first case we are dealing with a sphere, and in the second with a full-fledged ball with its contents inside.
- The sphere has its own area, but at the same time it has no volume. A sphere, on the other hand, is: its volume can be calculated, while it has no area. Someone may say that this is the main sign of difference, but it only manifests itself if it is necessary to make some calculations (complex geometric formulas). Therefore, the main difference is that the sphere is hollow, and the sphere is a body with contents inside.
- Another difference lies in the radius. For example, the radius of a sphere is not only the distance of points to the center. Any line segment connecting a point on a sphere with its center can be called a radius. All these segments are equal to each other. As for the ball, the points lying inside it are removed from the center by less than the radius (just because of the sphere that bounds it).
- The sphere is hollow, while the sphere is filled with a body. For example, a balloon is a sphere, a billiard ball is a full-fledged ball.
- The sphere has area and does not have volume, while the sphere is vice versa.
- The third difference is the measurement of the radius of two geometric bodies.