CN210488961U - Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid - Google Patents
Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid Download PDFInfo
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- CN210488961U CN210488961U CN201921053794.2U CN201921053794U CN210488961U CN 210488961 U CN210488961 U CN 210488961U CN 201921053794 U CN201921053794 U CN 201921053794U CN 210488961 U CN210488961 U CN 210488961U
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- rectangular pyramid
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Abstract
The utility model discloses a with teaching aid of ball end rectangular pyramid demonstration awl volume, ball surface area formula, including upper portion ball end regular rectangular pyramid (1), right part ball end regular rectangular pyramid (2), anterior ball end regular rectangular pyramid (3), lower part ball end regular rectangular pyramid (4), left part ball end regular rectangular pyramid (5) and rear portion ball end regular rectangular pyramid (6), its characterized in that: the teaching aid is characterized in that the vertexes of the upper spherical bottom regular rectangular pyramid (1), the right spherical bottom regular rectangular pyramid (2), the front spherical bottom regular rectangular pyramid (3), the lower spherical bottom regular rectangular pyramid (4), the left spherical bottom regular rectangular pyramid (5) and the rear spherical bottom regular rectangular pyramid (6) are intersected to form a sphere, and the sphere is combined and spliced to form the sphere-shaped teaching aid. The utility model discloses a just rectangular pyramid's of six ball bottoms plane laminating, the spheroid teaching aid is constituteed each other on the base sphere surface, and the simple and easy geometric shape body of rule is in order to do benefit to the demonstration directly perceived when teaching, deepens the student to the memory of abstract knowledge point in the textbook.
Description
Technical Field
The utility model belongs to the technical field of teaching equipment, relate to the teaching aid that proves awl volume, ball surface area formula with ball end rectangular pyramid particularly.
Background
On the premise that the education policy of China pays more attention to quality education and families in the society pay more attention to thinking culture of children, in the course of teaching by teachers, teaching can be scientifically carried out by combining teaching aids with abstract knowledge in textbooks, so that the enthusiasm and participation of students in class learning can be stimulated, and the abstract teaching knowledge can be more vivid, intuitive and easy to understand, so that the knowledge can be more firmly memorized; although the formulas of the cone volume, the sphere volume and the sphere surface area are demonstrated by adopting the exhaustive method, the differential method, the integral method, the subdivision method and the experimental method in the teaching field of mathematics, wherein the differentiation method and the integral method are more scientific, the formulas are too esoteric, not intuitive and difficult to understand for most of the students in the lower grades. In view of the above problems, it is necessary to demonstrate formulas of cone volume, sphere volume, and sphere surface area if a simple, intuitive, easy-to-learn teaching aid is available.
Disclosure of Invention
The utility model aims to overcome the defects, and provides a simple and visual teaching aid which is easy to speak and learn and uses a pyramid at the bottom of a sphere to prove the volume of the cone, the volume of the sphere and the formula of the surface area of the sphere.
The utility model discloses an aim at and solve its main technical problem and adopt following technical scheme to realize:
the utility model discloses a with teaching aid of ball end rectangular pyramid demonstration awl volume, ball surface area formula, including upper portion ball end regular rectangular pyramid (1), right part ball end regular rectangular pyramid (2), anterior ball end regular rectangular pyramid (3), lower part ball end regular rectangular pyramid (4), left part ball end regular rectangular pyramid (5) and rear portion ball end regular rectangular pyramid (6), wherein: the sphere is formed by intersecting the vertexes of an upper sphere bottom regular rectangular pyramid (1), a right sphere bottom regular rectangular pyramid (2), a front sphere bottom regular rectangular pyramid (3), a lower sphere bottom regular rectangular pyramid (4), a left sphere bottom regular rectangular pyramid (5) and a rear sphere bottom regular rectangular pyramid (6).
Four points at the bottoms of the six spherical bottom regular rectangular pyramids are sequentially connected to form the regular rectangular pyramids with the vertexes.
Any two of the six spherical bottom regular rectangular pyramids which are opposite to the center point of the cambered surface are connected to form three mutually vertical diameters.
Compared with the prior art, the utility model, possess obvious beneficial effect, can know by foretell technical scheme: the utility model discloses a spheroid teaching aid is constituteed to six positive rectangular pyramids in ball end, perhaps six three triangular pyramids in ball end constitute spheroid teaching aid, and its pyramid is the simple and easy geometry of rule for its simple structure easily understands, in order to do benefit to demonstration directly perceived more when teaching, deepens the student to the memory of abstract knowledge point in the textbook.
Drawings
FIG. 1 is an exploded view of the structure of the present invention;
FIG. 2 is a schematic structural view of the present invention;
FIG. 3 is a schematic structural view of a square pyramid with a spherical bottom according to the present invention;
fig. 4 is a schematic structural diagram 1 of a front spherical bottom regular rectangular pyramid, a lower spherical bottom regular rectangular pyramid, and a rear spherical bottom regular rectangular pyramid of the present invention;
fig. 5 is a schematic structural diagram 2 of the front spherical bottom regular rectangular pyramid, the lower spherical bottom regular rectangular pyramid, and the rear spherical bottom regular rectangular pyramid of the present invention.
The labels in the figure are:
1. the upper spherical bottom is a regular rectangular pyramid; 2. right spherical bottom regular rectangular pyramid; 3. the front spherical bottom is a regular rectangular pyramid; 4. The lower spherical bottom is a regular rectangular pyramid; 5. a right rectangular pyramid at the bottom of the left sphere; 6. the rear spherical bottom is a regular rectangular pyramid.
Detailed Description
In order to better understand the utility model, the technical scheme of the teaching aid for proving the cone volume, the ball volume and the ball surface area formula by using the pyramid with the ball bottom is described in detail below by combining the drawings and the preferred embodiments as well as the modes, the structures, the characteristics and the effects.
Referring to fig. 1-5, the utility model discloses a teaching aid of awl volume, ball surface area formula is proved with ball end rectangular pyramid, including upper portion ball end regular rectangular pyramid 1, right part ball end regular rectangular pyramid 2, anterior ball end regular rectangular pyramid 3, lower part ball end regular rectangular pyramid 4, left part ball end regular rectangular pyramid 5 and rear portion ball end regular rectangular pyramid 6, wherein: the top points of the upper spherical bottom regular rectangular pyramid 1, the right spherical bottom regular rectangular pyramid 2, the front spherical bottom regular rectangular pyramid 3, the lower spherical bottom regular rectangular pyramid 4, the left spherical bottom regular rectangular pyramid 5 and the rear spherical bottom regular rectangular pyramid 6 are intersected to form a sphere; the four points at the bottoms of the six spherical bottom regular rectangular pyramids are sequentially connected to form the regular rectangular pyramids with the vertexes; any two of the six spherical bottom regular rectangular pyramids which are opposite to the center point of the cambered surface are connected to form three mutually vertical diameters; the method for dividing the sphere into six rectangular pyramids comprises the following steps: the sphere bottom regular rectangular pyramid is formed by taking six end points of three diameters, which are mutually perpendicular and bisected, of spheres as the central points of six spherical surfaces, intersecting the central points to form 45 degrees to obtain four circumferential arc surrounding sphere bottom surfaces, and equally dividing the spheres into six spherical surfaces.
Referring to fig. 1-5, the first demonstration mode is that the vertexes of six regular rectangular pyramids with spherical bottoms are intersected at one point (the center of the sphere) to form a sphere, and the area of the spherical bottom of any regular rectangular pyramid with spherical bottom is
(formula of sphere surface area 4 π r2) The volume of any regular rectangular pyramid at the bottom of the ball is
(formula for sphere volume)
) Since the radius r of the sphere is the distance from the vertex to the surface of any sphere, the height h of any regular rectangular pyramid at the bottom of the sphere is the radius r, and the volume of any regular rectangular pyramid at the bottom of the sphere is
Thereby obtaining the pyramid conventional volume formula by verification
And the demonstration mode II is that a front spherical bottom regular rectangular pyramid 3, a lower spherical bottom regular rectangular pyramid 4 and a rear spherical bottom regular rectangular pyramid 5 are spliced, the lower spherical bottom regular rectangular pyramid 4 is used as a base, the middle of the front spherical bottom regular rectangular pyramid 3 and the middle of the rear spherical bottom regular rectangular pyramid 5 are cut into a half, two front spherical bottom regular rectangular pyramid 3 and two rear spherical bottom regular rectangular pyramid 5 are respectively spliced with the lower spherical bottom regular rectangular pyramid 4 into a hemisphere, and the hemisphere is formed by splicing the two parts of the front spherical bottom regular rectangular pyramid 3 and the rear spherical bottom regular rectangular pyramid 5 into a hemisphereHas a volume of
Volume of any spherical bottom regular rectangular pyramid
Thereby obtaining the pyramid conventional volume formula by verification
The volume of any regular rectangular pyramid at the bottom of the sphere is shown in the third demonstration mode
The sphere-shaped teaching aid composed of six regular rectangular pyramids with spherical bottoms has the volume
Thereby proving the volume of the sphere
The bottom area of any regular rectangular pyramid of the ball bottom is
The surface area of the sphere is
Thereby verifying the surface area S of the sphereBall with ball-shaped section＝4πr2。
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any form, and any simple modification, equivalent change and modification made by the technical spirit of the present invention to the above embodiments do not depart from the technical solution of the present invention.
Claims (3)
1. The utility model provides a prove with spherical bottom rectangular pyramid that the teaching aid of awl volume, ball surface area formula, includes upper portion spherical bottom regular rectangular pyramid (1), right part spherical bottom regular rectangular pyramid (2), anterior spherical bottom regular rectangular pyramid (3), lower part spherical bottom regular rectangular pyramid (4), left part spherical bottom regular rectangular pyramid (5) and rear portion spherical bottom regular rectangular pyramid (6), its characterized in that: the sphere is formed by intersecting the vertexes of an upper sphere bottom regular rectangular pyramid (1), a right sphere bottom regular rectangular pyramid (2), a front sphere bottom regular rectangular pyramid (3), a lower sphere bottom regular rectangular pyramid (4), a left sphere bottom regular rectangular pyramid (5) and a rear sphere bottom regular rectangular pyramid (6).
2. The teaching aid for demonstrating cone volume, sphere surface area formula with a spherical bottom pyramid as claimed in claim 1, wherein: four points at the bottoms of the six spherical bottom regular rectangular pyramids are sequentially connected to form the regular rectangular pyramids with the vertexes.
3. The teaching aid for demonstrating cone volume, sphere surface area formula with a spherical bottom pyramid as claimed in claim 1, wherein: any two of the six spherical bottom regular rectangular pyramids which are opposite to the center point of the cambered surface are connected to form three mutually vertical diameters.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201921053794.2U CN210488961U (en) | 2019-07-08 | 2019-07-08 | Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201921053794.2U CN210488961U (en) | 2019-07-08 | 2019-07-08 | Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN210488961U true CN210488961U (en) | 2020-05-08 |
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Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201921053794.2U Expired - Fee Related CN210488961U (en) | 2019-07-08 | 2019-07-08 | Teaching aid for proving cone volume, ball volume and ball surface area formula by using ball bottom rectangular pyramid |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN210488961U (en) |
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2019
- 2019-07-08 CN CN201921053794.2U patent/CN210488961U/en not_active Expired - Fee Related
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| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200508 Termination date: 20210708 |
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| CF01 | Termination of patent right due to non-payment of annual fee |