CN206441412U - Spheroid volume derives demonstration teaching aid - Google Patents
Spheroid volume derives demonstration teaching aid Download PDFInfo
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- CN206441412U CN206441412U CN201621051642.5U CN201621051642U CN206441412U CN 206441412 U CN206441412 U CN 206441412U CN 201621051642 U CN201621051642 U CN 201621051642U CN 206441412 U CN206441412 U CN 206441412U
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- cup
- bowl body
- bottom plate
- teaching aid
- radius
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Abstract
Demonstration teaching aid is derived the utility model discloses a kind of spheroid volume, belongs to higher mathematics teaching aid technical field.Bottom plate top left side, which is provided with inside cup of the top without capping, cup, is provided with solid cone, and bottom plate top right side is provided with the graduated scale being provided with the middle of bowl body of the top without capping, bottom plate top cup and bowl body perpendicular to bottom plate；Wherein, described cup is transparent column cup, and inner cylinder housing depth is the radius of cylindrical cavity bottom surface；Cone inside the cup is solid, identical highly with the radius of its bottom surface and highly identical with the cylindrical cavity of cup；Described bowl body is transparent hemisphere matrix bowl body, and the cylindrical cavity of hemisphere cavity radius and cup is highly identical；Described cup top surface and bowl body top surface are in the same plane.Specifically, vivid exhibition ball volume derivation method, intuitive is strong, is conducive to exciting the divergent thinking of student, is conducive to the interest of guiding student learning mathematicses, may advantageously facilitate the development of education activities.
Description
Technical field
The utility model is related to a kind of spheroid volume and derives demonstration teaching aid, belongs to higher mathematics teaching aid technical field.
Background technology
At present, higher mathematics is a more difficult course, comprising concept, property, proposition, theorem etc. relative take out
As, it is bad to understand, and in the teaching of higher mathematics, teaching aid application is also few.In order to make student more preferable in the study stage
Understanding, grasp and apply, the utility model provide a kind of spheroid volume derive demonstration teaching aid.
Utility model content
In order to solve the deficiency that above-mentioned prior art is present, the utility model provides a kind of spheroid volume and derives demonstration religion
Tool, intuitively helps student to understand the derivation method of spheroid volume, increases classroom vividness, promote Students ' Learning.
Its technical problem technical scheme for being used of the present utility model that solves is：A kind of spheroid volume derives demonstration religion
Tool, including cup, bottom plate, cone, graduated scale and bowl body, bottom plate top left side are provided with cup of the top without capping, cup
Inside is provided with solid cone, and bottom plate top right side is provided with the middle of bowl body of the top without capping, bottom plate top cup and bowl body
Provided with the graduated scale perpendicular to bottom plate；Wherein, described cup is transparent column cup, and inner cylinder housing depth is cylindrical cavity
The radius of body bottom surface；Cone inside the cup is solid, identical highly with the radius of its bottom surface, and with the circle of cup
Post housing depth is identical；Described bowl body is the cylindrical cavity height of transparent hemisphere matrix bowl body, hemisphere cavity radius and cup
Degree is identical；Described cup top surface and bowl body top surface are in the same plane.
The beneficial effects of the utility model are：The utility model solve current higher mathematics model teaching aid using less and
The problem of teaching method is single, specific, image exhibition ball volume derivation method, intuitive is strong, can be widely applied to mathematics
In teaching classroom, be conducive to exciting the divergent thinking of student, be conducive to the interest of guiding student learning mathematicses, may advantageously facilitate religion
The development of activity.
Brief description of the drawings
The utility model is further illustrated with reference to the accompanying drawings and detailed description.
Fig. 1 is structural representation of the present utility model.
Fig. 2 is the structural representation that the utility model adds colored solutions.
Fig. 3 is demonstration graph of the present utility model.
Label in figure：
1st, cup, 2, bottom plate, 3, cone, 4, graduated scale, 5, bowl body, 6, colored solutions.
Embodiment
As Figure 1-3, a kind of spheroid volume derives demonstration teaching aid, including cup 1, bottom plate 2, cone 3, graduated scale 4
With bowl body 5, the top left side of bottom plate 1 is provided with cup 1 of the top without capping, and the inside of cup 1 is provided with solid cone 3, and bottom plate 1 is pushed up
The scale being provided with the middle of bowl body 5 of the top without capping, the top cup 1 of bottom plate 1 and bowl body 5 perpendicular to bottom plate 1 is provided with the right side of portion
Chi 4；Wherein, described cup 1 is transparent column cup, and inner cylinder housing depth is the radius of cylindrical cavity bottom surface；It is described
Cone 3 inside cup 1 is solid, identical highly with the radius of its bottom surface, and with the cylindrical cavity height phase of cup 1
Together；Described bowl body 5 is transparent hemisphere matrix bowl body, and hemisphere cavity radius is highly identical with the cylindrical cavity of cup 1；It is described
The top surface of cup 1 and the top surface of bowl body 5 in the same plane.
Spheroid volume derivation method：
By injection colored solutions 6 in cup 1 and bowl body 5, the solution of left and right two is determined in sustained height by graduated scale 4,
Observe in cup 1 top surface area of colored solutions 6 in the top surface area of colored solutions 6 and bowl body 5.
As shown in Figure 3:
The top surface area of colored solutions 6 is in cup 1：
π(AB)2 –π(DC)2
The top surface area of colored solutions 6 is in bowl body 5：
π(HG) 2 =π(HF2 -FG2)= πHF2 -πFG2
Because HF=EF=AB, HF=AB
Because AD=FG, and AD=DC, so FG=DC
So π (AB)2 –π(DC)2=π(HG) 2
The cavity that cup 1 and cone 3 i.e. up and down in the same plane is constituted and hemisphere cavity body in bowl body 5,
Sectional area all same in any parallel surface.
According to ancestral's Geng principles
The cavity volume that the recessed cavity volume of hemisphere is formed with being removed in cup 1 after cone 3 is identical.
I.e.
Cylinder cavity volume-volume of cone 3 in hemisphere volume=cup 1
Hemisphere volume=
So as to derive that spheroid volume is。
Claims (2)
1. a kind of spheroid volume derives demonstration teaching aid, it is characterised in that：A kind of spheroid volume derives demonstration teaching aid, including cup
（1）, bottom plate（2）, cone（3）, graduated scale（4）And bowl body（5）, bottom plate（2）Top left side is provided with cup of the top without capping
Body（1）, cup（1）Inside is provided with solid cone（3）, bottom plate（2）Top right side is provided with bowl body of the top without capping（5）,
Bottom plate（2）Top cup（1）And bowl body（5）Centre is provided with perpendicular to bottom plate（2）Graduated scale（4）.
2. a kind of spheroid volume according to claim 1 derives demonstration teaching aid, it is characterised in that：Described cup（1）For
Transparent column cup, inner cylinder housing depth is the radius of cylindrical cavity bottom surface；The cup（1）Internal cone（3）
It is identical highly with the radius of its bottom surface for solid, and and cup（1）Cylindrical cavity it is highly identical；Described bowl body（5）For
Transparent hemisphere matrix bowl body, hemisphere cavity radius and cup（1）Cylindrical cavity it is highly identical；Described cup（1）Top surface
With bowl body（5）Top surface is in the same plane.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201621051642.5U CN206441412U (en) | 2016-09-13 | 2016-09-13 | Spheroid volume derives demonstration teaching aid |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201621051642.5U CN206441412U (en) | 2016-09-13 | 2016-09-13 | Spheroid volume derives demonstration teaching aid |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN206441412U true CN206441412U (en) | 2017-08-25 |
Family
ID=59645413
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201621051642.5U Expired - Fee Related CN206441412U (en) | 2016-09-13 | 2016-09-13 | Spheroid volume derives demonstration teaching aid |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN206441412U (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108346352A (en) * | 2018-01-22 | 2018-07-31 | 重庆工商职业学院 | Mathematical education verifies system |
-
2016
- 2016-09-13 CN CN201621051642.5U patent/CN206441412U/en not_active Expired - Fee Related
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108346352A (en) * | 2018-01-22 | 2018-07-31 | 重庆工商职业学院 | Mathematical education verifies system |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20170825 Termination date: 20190913 |