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Presentation on the topic "Round bodies: cylinder, cone, ball". Presentation on the topic "round geometric bodies" Presentation on the topic of round bodies in everyday life

  • 14.03.2020

The date: 23.12.2017

Teacher: Kuksenko Natalia Nikolaevna

Subject: maths

Class: 6

Topic: Round bodies

Formed UUD: the ability to plan ways to achieve the intended goals; the ability to adequately assess the degree of objective and subjective difficulty in completing a learning task

Target: to introduce students to geometric bodies: a ball, a cone, a cylinder - and their elements.

Tasks:

be able to operate with concepts: ball, cone, cylinder, base, height, vertex, sphere, center, radius, diameter, circular sector, section when performing various tasks; be able to recognize the studied geometric shapes; be able to give examples of objects that have the shape of the studied bodies of revolution; be able to talk about a ball, cone, cylinder according to plan.

During the classes:

Update

Oral survey.

1. The radii of the circles are 3 cm and 5 cm. What is their relative position if the distance between the centers is

a) 8 cm?; b) 10 cm; c) 6 cm; d) 0

2. Name equal elements in triangles.

a)

b)

2. Problematization (learning task)

Correctly read the statement, written without spaces: Mathematics is the queen of all sciences. Her beloved is truth, her people are simplicity and clarity. The palace of this mistress is surrounded by thorny thickets, and in order to achieve it, everyone has to wade through the thicket. A casual traveler will not find the water of the palace for nothing attractive.

goal setting

In this lesson, you will be introduced to three new geometric shapes. To better understand new material, be attentive, active and quick-witted. The topic of the lesson is encrypted with the help of puzzles. Solve them and you will find out what geometric shapes we will study today.

So, the topic of the lesson is "Round Bodies"

- Write the topic of the lesson in your notebook.

What is the purpose of our lesson?

4. Main body

1) Remember which figure was encrypted in the rebus in the form of a hat?

What other objects are cylindrical?

It turns out that the word "cylinder" comes from the Greek word "kyulindros", meaning "roller", "skating rink".

At the turn of the 18th - 19th centuries, men of many countries wore hard hats with small fields, which were called cylinders because of their great resemblance to the geometric figure of a cylinder.

Let's take a closer look at the cylinder (demonstration of the model) and see that the cylinder consists of two bases located in parallel planes and a side surface.

The cylinder is obtained by rotating a rectangle around one of its sides.

What are the bases of a cylinder?

What can you say about the size of these circles?

What is the side surface of a cylinder?

Look at the cylinder bore. What is the lateral surface of a cylinder?

The cylinder has parameters - this is the height and radius.

Let's try to formulate the definition of the height and radius of the cylinder.

So, height is a segment connecting the centers of the bases, perpendicular to each of them; cylinder radius - the radius of the circle that is the base of the cylinder.

Practical task.

Fold the side surface of the cylinder from a rectangular sheet. What is its height?

Imagine a situation where we need to cut a cylinder.

How can this be done and what happens in the cross section of the cylinder?

2) - And now we turn to the consideration of the cone.

The word "cone" comes from the Greek word "konos", meaning a pine cone (showing a cone). Indeed, there are some similarities.

What objects are shaped like a cone?

The cone consists of a base and a side surface.

A cone is obtained by rotating a right triangle around its side with a right angle.

What is the base of the cone?

What is the side surface?

What the side surface is like, we will see by turning the paper cone onto a plane. The lateral surface of the cone unfolds into a circular sector - a part of a circle bounded by two radii.

A cone has a vertex, height, base radius

Let's formulate a definition.

So, the height is a perpendicular drawn from the top of the cone to the center of the base.

If we cut off the vertex and the upper part of the cone (I show it on the model), then we will get the so-called truncated cone.

- Think and say, what objects have the shape of a cone or a truncated cone?

How is it possible to cut the cone and what happens in its cross section?

It turns out that the sections of the cone can have the shapes of other geometric shapes, the names of which we don’t even know yet, we will study them in high school, and therefore we won’t talk about them yet

3) -Let's move on to the study of the ball.

Give examples of surrounding objects that have the shape of a ball.

What do you think a ball and a circle and a circle have in common?

The ball is obtained by rotating a semicircle around the diameter.

The surface of the sphere is calledsphere.The word "sphere" comes from the Greek word "sfire", which is translated into Russian as "ball". Do not confuse the concepts of "ball" and "sphere". A sphere is, one might say, a shell or boundary of a sphere.

A ball, a globe are spheres, but a watermelon, an orange, the Sun, the Moon, the Earth and other planets have the shape of a slightly flattened ball (the picture shows).

Try to call the sections of the ball planes.

Which section will be the largest?

So, we got acquainted with three spatial figures, they are called differently geometric bodies. In 5th grade, you met polyhedrons. Let's remember their names.

Why are they called polyhedrons?

What would you call the new geometric bodies?

Indeed, all geometric bodies are divided into two groups: polyhedra and bodies of revolution.

Working with the textbook

7. Evaluation

- Summarize knowledge by completing a test in a notebook.

Task number 1. What form of objects is the tower made of? Name from top to bottom.

(Cone, cube, cylinder)

Task number 2. The figure shows various geometric bodies. Which of them are polyhedra?

Second (pyramid), third (tilted prism)

Task number 3. In the figure, the first line shows the front view of the figure, and the second line shows the top view of the figure. What is this figure?

1. Cone. 2.Cylinder. 3. Quadrangular pyramid. 4. Rectangular parallelepiped. 5. Triangular pyramid. 6. Ball.

Task number 4. There are three cones of different colors on the round table - red, blue and green. Children sit around the table: Masha, Vanya, Dasha, Kolya, Raya and Petya. Which of the children sees such a picture, as shown in the picture under the letter a); b); in)?

a B C)

(Petya) (Vanya) (Masha)

Task number 5. The figure shows some geometric bodies. Perhaps the point of view is not very familiar. What bodies, when viewed from the appropriate side, might look like the one in the figure? Which of the drawings can correspond to the same body?

1. Cube or box. 2. Pyramid or cone. 3. Cone, cylinder or ball. 4. Parallelepiped. Figures 2 and 3 may correspond to a cone, and figures 1 and 4 to a parallelepiped.

8. Reflection

If you think you understand the topic of the lesson, then draw a green circle.

If you think that you have not mastered the material enough, then draw a blue circle.

If you think you didn't understand the topic of the lesson, then draw a red circle.

9. Perspective (homework) № 446, 448

According to the definition adopted in 2006 by the International Astronomical Union, a planet is a body revolving around the Sun, massive enough to be spherical under the influence of its own gravity, in addition, it must have space near its orbit, free from other objects. If you pay attention to the first part of this formulation, then you can ask yourself - what is the minimum size of a body in general so that it has the shape of a ball?

It is believed that this figure is approximately 400 kilometers. At least in our solar system, the 397 km Mimas is spherical, making it the smallest round body known.


Mimas


At the same time, this indicator depends on what the body consists of - therefore, for icy satellites it is less, for stone objects it is more. For example, the 530-kilometer asteroid Hygiea is definitely not round. The 420-kilometer Proteus (satellite of Neptune) is also not at all like Mimas.


Proteus


The infographic below shows all round bodies solar system having a diameter of less than 10 thousand kilometers. This includes both spherical objects and bodies like Haumea and Varuna, which are elliptical in shape. Also, for some reason, the already mentioned Hygiea and Proteus were recorded everywhere - but even with them, I think the picture is quite clear.


Another version of the infographic that only includes the bodies that have been visited spacecraft. Both pictures are good to use for a visual comparison in order to understand what a huge part of the solar system we have not yet studied.

slide 2

Cylinder Cone Sphere Historical Facts Interesting Authors

slide 3

Cylinder A cylinder is a body bounded by a cylindrical surface and two circles with borders. Lateral surface - cylindrical surface Base - circles Generators - Generators of a cylindrical surface Axis - straight line OO1 Radius - radius of the base Height - length of the generatrix

slide 4

Section types:

Axial If the cutting plane passes through the axis of the cylinder, then the section is a rectangle, two sides of which are generatrices, and the other two are the diameters of the bases of the cylinder Circular If the cutting plane is perpendicular to the axis of the cylinder, then the section is a circle. A cylinder can be obtained by rotating a rectangle around one of its sides

slide 5

Cylinder surface area

The total surface area of ​​a cylinder is the sum of the areas of the lateral surface and the two bases. S=2πr(r+h) The area of ​​the lateral surface of the cylinder is equal to the product of the circumference of the base and the height of the cylinder. The area of ​​its development is taken as the area of ​​the lateral surface of the cylinder. S=2prh

slide 6

Historical note about the cylinder

CYLINDER.. The word "cylinder" comes from the Greek kylindros, which means "roller", "skating rink".

Slide 7

Cone Cone - A body bounded by a conical surface and a circle with a boundary. Conical surface - lateral surface of the cone Base - circle Generators of the cone - generatrix of the conical surface Axis - straight line passing through the center of the base and the top of the cone

Slide 8

Section types:

Axial - If the cutting plane passes through the axis of the cone, then the section is an isosceles triangle. The base of which is the diameter of the base of the cone, and the sides are the generatrix of the cone Circular - If the cutting plane is perpendicular to the axis of the cone, then the section is a circle. The cone can be obtained by rotating a right triangle around one of the legs.

Slide 9

Cone surface area

The area of ​​the full surface of the cone is called the sum of the areas of the lateral surface and the base S=πr(l+r) The area of ​​the lateral surface of the cone is equal to the product of half the circumference of the base and the generatrix. S=πrl The area of ​​its development is taken as the area of ​​the lateral surface of the cone.

Slide 10

Basic Formulas

  • slide 11

    Historical background about the cone

    CYLINDER.. The word "cylinder" comes from the Greek kylindros, which means "roller", "skating rink". CONE. The Latin word conus is borrowed from the Greek language (konos - plug, sleeve, pine cone). In the XI book of the "Beginnings" the following definition is given: if a right-angled triangle rotating around one of its legs returns to the same position from which it began to move, then the described figure will be a cone. Euclid considers only

    slide 12

    Sphere A sphere is a surface consisting of all points in space located at a given distance from a given point. A radius segment that connects the center to any point on the sphere A diameter segment that connects two points on a sphere and passes through its center. A chord is a segment that connects any two points on a sphere.

    slide 13

    Sphere area

    For the area of ​​the sphere, we take the limit of the sequence of areas of the surfaces of polyhedra circumscribed around the sphere as the largest size of each face tends to zero. S=4πR^2

    Slide 14

    Tangent plane to sphere

    A tangent plane to a sphere is a plane that has only one common point with the sphere. The point of contact is their common point. Theorem: The radius of the sphere, drawn to the point of contact between the sphere and the plane, is perpendicular to the tangent plane. Theorem: If the radius of a sphere is perpendicular to a plane passing through its end lying on the sphere, then this plane is tangent to the sphere

    slide 15

    Historical background about the sphere

    However, both the words "ball" and "sphere" come from the same Greek word "sfire" - ball. At the same time, the word "ball" was formed from the transition of consonants sph into sh. In ancient times, the sphere was held in high esteem. Astronomical observations of the firmament invariably evoke the image of a sphere. The Pythagoreans taught about the existence of ten spheres of the Universe, along which celestial bodies allegedly move. They argued that the distances of these bodies from each other are proportional to the intervals of the musical scale. In this they saw the elements of world harmony. Pythagorean "music of the spheres" was contained in such semi-mystical reasoning. Aristotle believed that the spherical shape, as the most perfect, is characteristic of the Moon, the Sun, the Earth and all world bodies. Developing the views of Eudoxus, he believed that the Earth is surrounded by a series of concentric spheres. The sphere has always been widely used in various areas science and technology. In Book XI of the Elements, Euclid defines a sphere as a figure described by a semicircle rotating about a fixed diameter.

    slide 16

    Vodovzvodnaya Tower The Vodovzvodnaya Tower was built in 1488. The former name of the tower - Sviblova - is associated with the courtyard of the boyar Sviblova located nearby. In 1633, a water pump was installed in the tower to pump water into a reservoir located on the top of the tower. Through the pipes, water dispersed throughout the Kremlin. In 1805-1806, the tower was dismantled and rebuilt according to the project of the architect I.V. Egotov. In 1812, the tower was blown up by the French, and in 1819 it was restored under the leadership of O.I. Bove. The height of the tower to the star is 57.7 meters, with the star - 61.25 meters. The tower is a cylinder. The tower is round in cross section.

    Slide 17

    Krivoarbatsky pereulok, building 10. Two huge white cylinders leaning against each other. Along the perimeter - sixty small diamond-shaped windows, creating the image of a beehive. On the facade there is a giant window several meters high. Above the window there is an inscription: "Konstantin Melnikov. Architect". The most famous (even iconic) building of the 1920s in Moscow. Konstantin Stepanovich Melnikov was born in Moscow in the family of a construction worker, a native of peasants, in 1890. After graduating from a parish school, he worked as a "boy" in a firm " Trading house Zalessky and Chaplin". Chaplin helped him enter the Moscow School of Painting, Sculpture and Architecture in 1905, and then, after graduating from Melnikov in 1913, the painting department advised him to continue his studies at the Architectural Department, which Konstantin Stepanovich graduated in 1917. At the senior courses of the School and in the first years after his graduation, Melnikov worked in the spirit of neoclassicism. However, already in the early 1920s, Konstantin Stepanovich sharply broke with various kinds of traditionalist stylizations. The very fact of the wide implementation of his works makes us take a different attitude towards those of his works that remained in projects and which in the 20s, in the sharp controversy of that period, were often declared "fantastic". In Melnikov's projects, the degree of uninhibited creative imagination of the master in matters of shaping is striking. It can be said with full confidence that in the 20th century there was no other architect who created there would be so many fundamentally new projects and such a level of novelty that their originality not only severely separated them from the works of other masters, but also distinguished them just as strongly from the works of their author himself.









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    slide 1

    ROUND BODIES / press conference / CYLINDER CONE BALL Presentation for a geometry lesson in grade 11.

    slide 2

    Generalization and deepening of knowledge about round bodies; their application (round bodies) in practice in everyday life; Development of logical thinking, creative activity, speech; Education of independence, activity, culture of communication. LESSON OBJECTIVES

    slide 4

    BALL, SPHERE I am a globe, an orange and a ball. I - round ball, I'm even a teapot.

    slide 5

    CONE You will find me easily in a funnel, On a Christmas tree, in a hat near a mushroom. Yes, the cone does not stand aside, Carrot is also me.

    slide 6

    TRUNCATED CONE Factory chimney and illuminated beacon - This cone is not at all simple - truncated!

    Slide 7

    Here is a task not for the timid: Pack the ball in a box. It must fit tightly, so as not to shake it on the way.

    Slide 8

    And in the end? Look: the cube is a box, the ball is inside.

  • Slide 9

    Geometry: Proc. for 10-11 grades of secondary school / L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev and others - M .: Education. 2007 Microsoft Office power point/collection of pictures/ http://iskystvo.ru/2008/10/ Used literature and Internet resources:

    View all slides

    Abstract

    2. Educational institution.

    3. Geometry, grade 11

    5. Lesson topic. " Cylinder, cone, ball » /PRESS CONFERENCE/

    Bibliography.

    http://www.salda.ru/dishes/profi/

    http://www.cook.freecopy.su/cookbook/?l=23&w=4306

    http://www.srbp.ru/offers/20/805/2456.html

    http://fotki.yandex.ru/users/mamuka532/view/60544/

    http://arsel.flamber.ru/photos/1200076904/

    http://www.vikar-plastic.com.ua/index.php?categoryID=301

    http://yogaclassic.ru/post/2343

    http://fantasyflash.ru/anime/index.php?kont=sea&n=3

    http://fantasyflash.ru/anime/index.php?kont=disney&n=1

    http://www.liveinternet.ru/photo/ha8xa7/post15454746/

    http://s99-omsk.narod.ru/projects/v/mozaika.htm

    http://iskystvo.ru/metka/forma/

    http://www.russika.ru/ef.php?s=3346

    http://akinfeev.livejournal.com/17482.html?page=26

    http://mega.km.ru/bes_2004/encyclop.asp?TopicNumber=34130&rubr=156

    http://www.board74.ru/articles/geometry/tcone.html

    http://iskystvo.ru/2008/10/

    http://flamber.ru/photos/tags/%E4%EE%F0%EE%E3%E0/1181070512/

    http://slavyane.cddk.ru/publ/20-1-0-272

    http://media.meta.ua/files/pic/0/26/108/mIR6YnZXGo.jpg

    pot

    orange

    animations (lighthouse)

    animations (mickey and princess)

    frustum

    factory pipe

    2. Educational institution. Municipal educational institution "Secondary school No. 15 of the village of Berezayka" Bologovsky district of the Tver region

    3. Subject, class in which the product is used. Geometry, grade 11

    5. Lesson topic. " Cylinder, cone, ball » /PRESS CONFERENCE/

    6. Necessary equipment and materials for the lesson. Models of round bodies, "black box" for riddle questions, interactive board to view a presentation or multimedia installation.

    7. Description of multimedia product. The presentation was created using the Power Point office application. Change of slides is carried out by mouse click. Content of the presentation: topic of the lesson, goals, followed by slides representing a cylinder, a ball, a cone, a truncated cone, which were created together with students answering questions during a press conference. Next is a slide on which a question of practical content is written, then the answer to it, the results of the lesson and a list of Internet resources. The slides contain pictures and photographs borrowed from the Internet. Formulas, poems compiled by the author of the work

    8.The purpose of creating and using a media product in the classroom. For better visibility. The lesson is designed to be open.

    9. How is it implemented in the lesson (time and place). It is used at the beginning of the lesson when setting goals and introducing children - representatives of scientific societies: "Cylinder", "cone", "ball", "truncated cone". Then used after summarizing the first part of the lesson, when students begin to complete practical task(fit a sphere into a cube). At the end of the lesson when debriefing.

    Bibliography.

    1.Altypov P.I. Geometry. Tests. 10-11 cells: educational method. allowance.-M.: Bustard, 2001

    2. Ziv B.G. Tasks for geometry lessons grade 7-11. - St. Petersburg, 2000, ed. "Acacia"

    3. Geometry: Proc. for 10-11 grades of secondary school / L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev and others - M .: Education. 2007

    4. Encyclopedic Dictionary of a Young Mathematician / compiled by A.P. Savin.-M.6 Pedagogy, 1989

    5. INTERNET resources (list of pictures in order)

    http://www.salda.ru/dishes/profi/

    http://www.cook.freecopy.su/cookbook/?l=23&w=4306

    http://www.srbp.ru/offers/20/805/2456.html

    http://fotki.yandex.ru/users/mamuka532/view/60544/

    http://arsel.flamber.ru/photos/1200076904/

    http://www.vikar-plastic.com.ua/index.php?categoryID=301

    http://yogaclassic.ru/post/2343

    http://fantasyflash.ru/anime/index.php?kont=sea&n=3

    http://fantasyflash.ru/anime/index.php?kont=disney&n=1

    http://www.liveinternet.ru/photo/ha8xa7/post15454746/

    http://s99-omsk.narod.ru/projects/v/mozaika.htm

    http://iskystvo.ru/metka/forma/

    http://www.russika.ru/ef.php?s=3346

    http://akinfeev.livejournal.com/17482.html?page=26

    http://mega.km.ru/bes_2004/encyclop.asp?TopicNumber=34130&rubr=156

    http://www.board74.ru/articles/geometry/tcone.html

    http://iskystvo.ru/2008/10/

    http://flamber.ru/photos/tags/%E4%EE%F0%EE%E3%E0/1181070512/

    http://slavyane.cddk.ru/publ/20-1-0-272

    http://media.meta.ua/files/pic/0/26/108/mIR6YnZXGo.jpg

    pot

    orange

    animations (lighthouse)

    animations (mickey and princess)

    frustum

    To enjoy preview presentations create an account ( account) Google and sign in: https://accounts.google.com


    Slides captions:

    Round bodies Presentation for a lesson in mathematics in the 6th grade Completed by Tremasova Tamara Nikolaevna MOU "SOSHp. Gorny Krasnopartizansky district of the Saratov region"

    Cylinder - translated from Greek means "roller"

    The surface of the cylinder consists of two bases and a side surface reamer

    Sections of a cylinder by an inclined plane

    Cylinder - formed by a rectangle rotating around one of the sides

    The cone is translated from ancient Greek as "cone", "top".

    The base of the cone is a circle. base

    Cone sections - triangle, circle, ellipse.

    Cone - formed by a right triangle rotating around one of the legs

    Diameter A sphere, like a circle, has a center, a radius, and a diameter.

    Sphere-surface of a ball (like a ball shell, orange peel)

    When a sphere is cut by a plane, only a circle is obtained.

    Ball - formed by a semicircle rotating around the diameter of the cut

    Literature Literature and Internet resources Mathematics: Proc. for 5 cells. general education institutions /G.V. Dorofeev, S.B. Suvorova, E.A. Bunimovich and others; Ed. G.V. Dorofeeva, I.F. Sharygin. - 2nd ed., revised. - M.: Education, 2010. - 288 p.: ill. Mathematics: Proc. for 6 cells. general education Institutions / N.Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I. Schwarzburd. – 6th ed. - M.: Mnemosyne, 2000. - 304 p.: ill. First steps in geometry. Sharygin I.F., Erganzhieva L.N. visual geometry. 5 - 6 cells: A manual for general educational institutions. – 3rd ed., stereotype. - M.: Bustard, 2000. - 192 p.: ill. http://uztest.ru/abstracts/?idabstract=970 472 http://vio.uchim.info/Vio_30/cd_site/articles/art_3_5.htm http://www.uchportal.ru/load/25-1- 0-25920

    Thank you for your attention!


    On the topic: methodological developments, presentations and notes

    §one. COMBINATIONS OF THE BALL WITH POLYHEDRALS. THEOREM 1.1. Through any four points that do not belong to the same plane, one and only one can be drawn ...


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