What is the difference between a circle and a ball? Circle and ball - what's the difference? — Useful information for everyone. How does a ball differ from a sphere? Difference between ball and sphere

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Presentation for the lesson

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Target: introduce children to geometric shapes (ball and cube). Create conditions for consolidating the ability to distinguish and name a ball (ball) and a cube (cube).

Tasks:

• teach children to distinguish and name geometric shapes (ball and cube);
• develop memory and mental operations in children (analysis, comparison);
• develop speech;
• practice counting to five;
• practice sculpting techniques;
• cultivate cognitive activity;

Preliminary work:

With kids: Introducing the circle and square. Comparison of geometric shapes (circle and square). Exercise in mental counting to five. Reinforcing sculpting techniques. Preparing a slide presentation for class.

With parents: Conversation with parents about asking their children at home more often the questions “What objects are like a circle?”, “What objects are like a square?”

List of didactic material: Slides with tasks: “What is the difference between a circle and a square?”, “What is the difference between a ball and a cube?”, “How many red balls?”, “How many green cubes?”, “How many cubes in total?”, slide with dynamic pause, slides with sculpting techniques.

Equipment: screen for playing slides, projector.

Materials: oilcloths for modeling with plasticine and plasticine of the same color for each child.

Slide 1.

Educator: Hello children. Do you like surprises? I have a surprise for you. Look who came to visit us.

Slide 3.

Children: These are cubes and balls.

Slide 4.

Educator: Let's take a closer look at the balls and cubes.

Slide 5.

Educator: What shape does the ball already know to you resemble?

Children: To the circle.

Educator: Right on the circle.

Slide 6.

Educator: What figure does a cube already know to you resemble?

Children: Per square.

Educator: Right on the square.

Slide 7.

Educator: Look carefully and remember the difference between a circle and a square.

Slide 8.

Educator: What does a square have that a circle doesn't?

Children: A square has corners. A circle has no corners.

Educator: Right. A circle and a square have different angles.

Slide 9.

Educator: Think and tell me the difference between a ball and a cube.

Slide 10.

Children: A ball and a cube have different angles.

Educator: The ball has no corners and therefore can be rolled.

Slide 11.

Educator: The cube has corners, this gives it stability and therefore you can build from cubes.

Children: Yes!

Educator: Be careful!

Slide 13.

Educator: How many red balls? Let's count together. I show, you name.

Children: One two.

Educator: Well done!

Slide 14.

Educator: How many green cubes? Let's count together.

Children: One two three four.

Educator: Well done!

Slide 15.

Educator: How many cubes are there in total? Let's count together.

Children: One two three four five.

Educator: You think well! Now let's play.

Slide 16.

Physical education minute.

Educator:

We sat quietly,
And now let's all stand together
(children stand near their chairs)
Let's stomp our feet,
(children stomp)
Let's clap our hands.
(children clap)
We'll take the cube from the floor
And let's put it again.
(children take cubes from the floor and place them on the other side)
We will take the ball in our hands -
We'll pass it on to someone else.
(children pass the ball around)
Now let's squeeze our fingers
(children clench and unclench their fingers)
And then we’ll start sculpting.

Slide 17.

Educator: Please sit down at your workstations to begin sculpting. We will make a cube and a ball.

(children sit at prepared tables with oilcloths and pieces of plasticine)

Educator: First you need to divide the plasticine into two parts.

Slide 18.

Educator: Take one piece of plasticine and shape it into a round shape by rolling it in a circular motion between your palms.
You already know how to do this and did it well. Check if your ball is rolling.

Slide 19.

Educator: Now the task is more difficult - you need to make a cube. Be careful: roll out a piece of plasticine using longitudinal movements of your palms and flatten it with your fingers to obtain the desired shape.
Well, did you manage? Check if your cube is standing firmly.

Slide 20.

Educator: See how Mishka enjoys your balls and cubes!
– I’m also very happy with your work!
– But remind me – what is the difference between a ball and a cube?

Children: The ball is round and rolls, and the cube has corners and stands firmly.

Educator: Right. Did you like the lesson?

Children: Yes!

Educator: And I liked it. You are simply great. Goodbye!

When people are asked the difference between a sphere and a ball, many simply shrug their shoulders, thinking that in fact they are the same thing (the 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? A sphere has some differences from a ball, which not only schoolchildren need to know in order to get a good grade for their demonstrated knowledge, but also many other people, for example, whose work is directly related to drawings.

Definition

Ball– the set of all points in space. All these points are located from the center of the geometric body at a distance that is no 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 involves entire geometric formulas that are very complex, despite the apparent simplicity of the geometric figure itself.

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 the shell of a ball without any content (more specific examples will be given below). Just like a ball, a sphere is a body of rotation. By the way, many also wonder what is the difference between a circle and a circle 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.

Comparison

It has already been said that a sphere is the surface of a ball, which already makes it possible to talk about one significant sign of 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 the surface (a sphere that is empty inside). In other words, the sphere is hollow. Usually, for ease of understanding, a simple example is given 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 own contents inside.
• A sphere has its own area, but it has no volume. A sphere is the opposite: its volume can be calculated, while it has no area. Some may say that this is the main sign of difference, but it only appears if it is necessary to make some calculations (complex geometric formulas). Therefore, the main difference is that the sphere is hollow, and the ball 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. A radius can be any segment connecting a point on a sphere to its center. 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 a radius (precisely because of the sphere bounding it).

Conclusions website

1. A sphere is hollow, while a ball is a body filled inside. For example, a hot air balloon is a sphere, a billiard ball is a full-fledged ball.
2. A sphere has area and no volume, but a sphere does the opposite.
3. The third difference is the measurement of the radius of two geometric bodies.

To obtain a competent answer to the question in the title, the reader of the article will need to thoroughly strain his abilities for abstract thinking and delve deeply into certain branches of mathematics that he had the opportunity to study at school. And to stimulate the imagination, it would be useful to recall that “Education is what remains after everything that we have been taught is forgotten” (the authorship of the phrase is attributed to A. Einstein).

A short dive into one of the branches of mathematics

First, you need to remember the existence of the science of geometry (in a somewhat loose translation from Greek, this word means “land surveying”) - a separate branch of mathematics specializing in the study of spatial structures, their relationships among themselves and various generalizations arising from this. It is important that despite such a “mundane” origin of the name, this science operates with purely abstract concepts that in the world we are familiar with do not exist in direct physical embodiment.

One of these basic concepts is geometric point. Use your imagination: unlike a “pencil dot”, “pin dot” and so on, this dot is a completely abstract object in imaginary space without any measurable characteristics such as “thickness”, “color” and so on (mathematics they like to pronounce the phrase “zero-dimensional object”). In principle, everything else in geometry will be further determined based on this abstraction.

The next concept needed for further discussion is the “ritual” mathematical phrase “geometric locus of points” (GMT). With its help, a certain set (collection) of points that fall under a certain relation (property) is described - thus a “geometric figure” is defined. Example: sphere (from the ancient Greek σφαῖρα, originally meaning ball/sphere) is the locus of such points in space that can be described as equidistant (being exactly the same distance) from some given point, usually called the “center of the sphere.”

The distance from the center of the sphere to this GMT is usually called the “radius of the sphere.” During all these manipulations, it is important to continue to remember that the sphere is a more ephemeral concept than even the familiar and familiar soap bubble: any soap bubble still has a quite tangible wall of water-soap film of microscopic thickness, which can be physically measured (and even pierce), but the sphere does not!

Now let's turn to the definition of a ball: a ball is understood as the collection of all such points in space that are located from a certain point (the center of the ball) at a distance not greater than a given one (the radius of the ball). In other words, a ball is a “geometric body” - one that, according to Euclid’s primary definition, “has length, width and depth” (in modern textbooks this definition is less clear: “a part of space limited by its formed shape”).

In passing, we note that the methods used here for defining a sphere and a ball through the center and radius are not the only ones: for example, defining a sphere/ball in space can be done by rotating a circle, a circle, etc. (those deeply interested in this issue are strongly recommended to familiarize themselves with a separate section of geometry called “Figures and bodies of revolution”, since this is a frequently used way of defining a wide variety of geometric figures and bodies in space).

Thus, both in the case of a sphere and in the case of a ball one has to deal with a certain geometric location of points (that is, a geometric figure), but only in the case of a ball can one speak of a geometric body. It is interesting to note that, strictly speaking, a sphere can be “subtracted” from a ball: in this case, mathematicians speak of an “open ball”. However, “by default” there is a “closed ball”, where the sphere is its natural boundary and part that belongs to it.

Summary

Both the ball and the sphere are abstract geometric objects (geometric figures), defined through some geometric locus of points in space - for example, using the concept of the center of the ball/sphere and the radius of the ball/sphere. However, only a ball is a full-fledged geometric body, since it includes not only a description of the surface that bounds it, but also the entire part of space that this surface contains. From this point of view, the sphere is only the external abstract boundary (surface) of a ball defined in space.

If you take a semicircle or circle and rotate it around its axis, you get a body called a ball. In other words, a ball is a body bounded by a sphere. A sphere is the shell of a ball, and its cross-section is a circle. A ball and a sphere are interchangeable bodies, unlike a cone, despite the fact that the cone is also a body of revolution. An infinite number of circles or circles can pass through two points A and B, located anywhere on the surface of the ball. This formula can be useful if either the diameter or radius of a ball or sphere is known. However, these parameters are not given as conditions in all geometric problems.

If the length of the diameter of the sphere (d) is known, then to find its surface area (S), square this parameter and multiply by the number Pi (π): S=π∗d². For example, with a sphere radius of three meters, its area will be 4∗3.14∗3²=113.04 square meters. To calculate the area of ​​a sphere using data, for example, from the second step, the search query that must be entered into Google will look like this: “4*pi*3^2”. And for the most complex case with calculating the cube root and squaring from the third step, the request will be: “pi*(6*500/pi)^(2/3)”.

Difference between ball and sphere

When people are asked the difference between a sphere and a ball, many simply shrug their shoulders, thinking that in fact they are the same thing (the analogy with a circle and a circle).

In everyday life we ​​rarely say sphere, more often ball or ball. And not everyone understands the difference between these two geometric concepts. We can probably say that the sphere is the outer shell of the ball. A balloon, for example, is not actually a ball, but a sphere. Provided, of course, that it is absolutely “round”. As I understand it, on a ball absolutely all points on the surface are equidistant from its center, but on a spherf this condition is not mandatory.

Orange, soccer ball, watermelon, similar to a ball. Of all bodies of a given volume, a ball has the smallest surface area. The surface of a ball is called a sphere. The distance from the points of a sphere to its center is called the radius of the sphere and is usually denoted by R. The radius is also called any segment connecting a point on the sphere with its center.

Definition: A ball segment is a part of a ball that is cut off from the ball by a cutting plane. The basis of the segment is called the circle that is formed at the section. I am the owner and author of this site, I wrote all the theoretical material, and also developed online exercises and calculators that you can use to study mathematics.

Any diameter corresponds to 2 radii. The part of a ball (sphere) that is cut off from it by any plane (ABC) is a spherical segment. Circles ABC and DEF are the bases of the spherical belt. The distance NK between the bases of the spherical belt is its height. 1/3 of the product of the surface area of ​​the ball and the length of the radius. It is often stated as follows: the volume of a ball is equal to 1/3 of the product of the surface of the ball and its radius.

All these points are located from the center of the geometric body at a distance that is no more than a given one. This distance itself is called the radius. All points in space are equidistant from the center of the sphere.

The formed figure will be a ball. Therefore, the ball is also called a body of rotation. Let's take some plane and cut our ball with it. Just like we cut an orange with a knife. The piece that we cut off from the ball is called a spherical segment.