CN105427714A - Instrument for verifying volume relations among sphere, cone and cylinder - Google Patents
Instrument for verifying volume relations among sphere, cone and cylinder Download PDFInfo
- Publication number
- CN105427714A CN105427714A CN201610005728.2A CN201610005728A CN105427714A CN 105427714 A CN105427714 A CN 105427714A CN 201610005728 A CN201610005728 A CN 201610005728A CN 105427714 A CN105427714 A CN 105427714A
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- hollow
- connecting pipe
- cone
- cylinder
- solenoid valve
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- G—PHYSICS
- G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
- G09B—EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS
- G09B23/00—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes
- G09B23/02—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics
- G09B23/04—Models for scientific, medical, or mathematical purposes, e.g. full-sized devices for demonstration purposes for mathematics for geometry, trigonometry, projection or perspective
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- General Physics & Mathematics (AREA)
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- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
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- Engineering & Computer Science (AREA)
- Mathematical Physics (AREA)
- Geometry (AREA)
- Business, Economics & Management (AREA)
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Abstract
The invention discloses an instrument for verifying volume relations among a sphere, a cone and a cylinder. The instrument comprises a combination container internally provided with a liquid and a support, the combination container comprises a hollow cone, a hollow ball, a hollow cylinder, a first connecting pipe and a second connecting pipe. The hollow cone with its bottom surface oriented upwards is arranged upside down right above the hollow ball, the hollow cylinder is arranged right below the hollow ball, the top end of the hollow cone and the top portion of the hollow ball are connected through the first connecting pipe, and the bottom portion of the hollow ball and the central portion of the top surface of the hollow cylinder are connected through the second connecting pipe; the diameter of the bottom surface of the hollow cone is equal to its height, is equal to the diameter of the bottom surface and the height of the hollow cylinder and is equal to the diameter of the hollow ball; the total volume of the liquid is equal to the volume of the hollow cone; and the first connecting pipe and the second connecting pipe are respectively provided with a first solenoid valve and a second solenoid valve, and the support is provided with a solenoid valve controller. The instrument provided by the invention can be applied to demonstration experiments of geometry mathematics, helps to improve the classroom teaching effect and can also replace a conventional hourglass for timing.
Description
Technical field
The present invention relates to a kind of maths demonstration experimental apparatus, be specially a kind of spheroid cone cylinder volume relation validating instrument.
Background technology
Spheroid, cone, cylindrical cubature formula and prove elementary geometry teaching a difficult point.When waiting end contour, the volume of cone is 1/3rd of cylinder volume, the volume of ball be then with its great circle be the end, diameter is for 2/3rds of high cylinder volume.If method validation above-mentioned relation by experiment, then can be derived from other cubature formula of two by the volume computing formula of any one in above-mentioned three kinds of solids, it is vivid for becoming abstract simultaneously, the learning interest of increase student.At present, lack a kind of be not only convenient for carrying with class demonstration, but also can fast verification spheroid, cone, cylinder volume relation maths demonstration experimental apparatus.
Summary of the invention
Object of the present invention is a kind of spheroid cone cylinder volume relation validating instrument for geometry teaching lecture experiment of exploitation.
In order to solve the problems of the technologies described above, the present invention by the following technical solutions:
A kind of spheroid cone cylinder volume relation validating instrument, comprise the combination container of built-in liquid and be fixed on the outer support closing container for protection group of combination container, described combination container comprises hollow cone, hollow ball, hollow cylinder, the first connecting pipe, the second connecting pipe; Stand upside down upward and be located at directly over hollow ball in hollow cone bottom surface, hollow cylinder is located at immediately below hollow ball, hollow cone top is all had aperture with hollow ball top and is connected by the first connecting pipe, all has aperture and connected by the second connecting pipe bottom hollow ball, in the middle part of hollow cylinder end face; The basal diameter of described hollow cone and highly equal, equals hollow cylinder basal diameter and height, equals the diameter of hollow ball; For convenience of observing, described liquid is colored liquid, and its cumulative volume equals the volume of hollow cone; Described first connecting pipe and the second connecting pipe are respectively equipped with the first solenoid valve and second solenoid valve of control first connecting pipe and the second connecting pipe pipeline break-make, support is provided with the solenoid valve controller of control first solenoid valve and the second solenoid valve, and solenoid valve controller is connected with the second solenoid valve electricity with the first solenoid valve.
Described support is also provided with the length scales for reading hollow cone, hollow ball, hollow cylinder geometric size and liquid level position.
Before starting experiment, liquid is all positioned at hollow cone, and the first solenoid valve and the second solenoid valve are in closure state.Press solenoid valve controller switch, open the first solenoid valve and open the first connecting pipe, flow direction hollow ball.When liquid all flows into hollow ball, just in time fill half hollow ball.Then solenoid valve controller is opened the second solenoid valve and is opened the second connecting pipe, flow direction hollow cylinder.When liquid all flows into hollow cylinder, liquid level is just in time positioned at 1/3rd positions of hollow cylinder height.Thus by experiment, verify above-mentioned cone, spheroid, cylindrical volume relationship, and cylindrical volume computing formula can be utilized to release the cubature formula of spheroid and cone.
The present invention, owing to adopting above-mentioned design, has both facilitated teacher to carry, again can fast verification spheroid, cone, cylinder volume relation, can be used for geometry teaching lecture experiment, is conducive to improving classroom teaching effect.The present invention can also replace traditional hourglass for timing, utilizes liquid to flow into spheroid from cone different with from the spheroid inflow cylindrical time, forms two period clocking capability.
Accompanying drawing explanation
Below in conjunction with accompanying drawing, the invention will be further described.
Fig. 1 is formation schematic diagram of the present invention (when liquid is all positioned at cone).
Fig. 2 is checking cone spheroid volume relationship schematic diagram (when liquid is all positioned at spheroid).
Fig. 3 is checking spheroid cylinder volume relation schematic diagram (when liquid is all positioned at right cylinder).
In figure: 1. hollow cone, 2. hollow ball, 3. hollow cylinder, 4. the first connecting pipe, 5. the second connecting pipe, 6. liquid, 7. support, 41. first solenoid valves, 45. solenoid valve controllers, 51. second solenoid valves, 71. length scales.
Embodiment
As shown in Figure 1; the present invention includes the combination container of built-in liquid 6 and be fixed on the outer support 7 closing container for protection group of combination container; combination container comprises hollow cone 1, hollow ball 2, hollow cylinder 3, first connecting pipe 4, second connecting pipe 5; stand upside down upward and be located at directly over hollow ball 2 in hollow cone 1 bottom surface; hollow cylinder 3 is located at immediately below hollow ball 2; hollow cone 1 top is all had aperture with hollow ball 2 top and is connected by the first connecting pipe 4, all has aperture and connected by the second connecting pipe 5 bottom hollow ball 2, in the middle part of hollow cylinder 3 end face.The basal diameter of hollow cone 1 and highly equal, equals basal diameter and the height of hollow cylinder 3, equals the diameter of hollow ball 2.For convenience of observing, liquid 6 is colored liquid, and its cumulative volume equals the volume of hollow cone 1.First connecting pipe 4 and the second connecting pipe 5 are respectively equipped with the first solenoid valve 41 and the second solenoid valve 51 of control first connecting pipe 4 and the second connecting pipe 5 pipeline break-make, support is provided with the solenoid valve controller 45 of control first solenoid valve 41 and the second solenoid valve 51, and solenoid valve controller 45 is connected with the second solenoid valve 51 electricity with the first solenoid valve 41.
Support 7 is also provided with the length scales 71 for reading hollow cone 1, hollow ball 2, hollow cylinder 3 physical dimension and liquid level position.
As shown in Figure 2, the liquid of original position in hollow cone 1 all flows in hollow ball 2, and now liquid 6 just in time fills the half of hollow ball 2 volume.
As shown in Figure 3, liquid 6 all flows in hollow cylinder 3, and now liquid level is just in time positioned at 1/3rd positions of hollow cylinder 3 height.
Claims (2)
1. a spheroid cone cylinder volume relation validating instrument, comprise the combination container of built-in liquid and be fixed on the outer support closing container for protection group of combination container, it is characterized in that: described combination container comprises hollow cone, hollow ball, hollow cylinder, the first connecting pipe, the second connecting pipe; Stand upside down upward and be located at directly over hollow ball in hollow cone bottom surface, hollow cylinder is located at immediately below hollow ball, hollow cone top is all had aperture with hollow ball top and is connected by the first connecting pipe, all has aperture and connected by the second connecting pipe bottom hollow ball, in the middle part of hollow cylinder end face; The basal diameter of described hollow cone and highly equal, equals hollow cylinder basal diameter and height, equals the diameter of hollow ball; Described liquid is colored liquid, and its cumulative volume equals the volume of hollow cone; Described first connecting pipe and the second connecting pipe are respectively equipped with the first solenoid valve and second solenoid valve of control first connecting pipe and the second connecting pipe pipeline break-make, support is provided with the solenoid valve controller of control first solenoid valve and the second solenoid valve.
2. a spheroid cone cylinder volume relation validating instrument, is characterized in that: described support is also provided with the length scales for reading hollow cone, hollow ball, hollow cylinder geometric size and liquid level position.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610005728.2A CN105427714A (en) | 2016-01-05 | 2016-01-05 | Instrument for verifying volume relations among sphere, cone and cylinder |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610005728.2A CN105427714A (en) | 2016-01-05 | 2016-01-05 | Instrument for verifying volume relations among sphere, cone and cylinder |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN105427714A true CN105427714A (en) | 2016-03-23 |
Family
ID=55505887
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610005728.2A Pending CN105427714A (en) | 2016-01-05 | 2016-01-05 | Instrument for verifying volume relations among sphere, cone and cylinder |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105427714A (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SU619950A1 (en) * | 1976-09-02 | 1978-08-15 | Горловский Филиал Донецкого Ордена Трудового Красного Знамени Политехнического Института | Mathematics visual aid |
| CN202033919U (en) * | 2011-01-10 | 2011-11-09 | 马秋成 | Demonstration device for volume relationship between cone and cylinder |
| CN202795830U (en) * | 2012-09-30 | 2013-03-13 | 许明明 | Circular cone volume formula calculus instrument |
| CN204066512U (en) * | 2014-07-26 | 2014-12-31 | 刘季 | Cylinder with cone volume relationship demonstration teaching aid |
| CN204242460U (en) * | 2014-09-12 | 2015-04-01 | 嵇振宇 | A kind of Novel teaching device |
| CN204440755U (en) * | 2015-02-15 | 2015-07-01 | 马玺渊 | A kind of volume relationship demonstration teaching aid |
-
2016
- 2016-01-05 CN CN201610005728.2A patent/CN105427714A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SU619950A1 (en) * | 1976-09-02 | 1978-08-15 | Горловский Филиал Донецкого Ордена Трудового Красного Знамени Политехнического Института | Mathematics visual aid |
| CN202033919U (en) * | 2011-01-10 | 2011-11-09 | 马秋成 | Demonstration device for volume relationship between cone and cylinder |
| CN202795830U (en) * | 2012-09-30 | 2013-03-13 | 许明明 | Circular cone volume formula calculus instrument |
| CN204066512U (en) * | 2014-07-26 | 2014-12-31 | 刘季 | Cylinder with cone volume relationship demonstration teaching aid |
| CN204242460U (en) * | 2014-09-12 | 2015-04-01 | 嵇振宇 | A kind of Novel teaching device |
| CN204440755U (en) * | 2015-02-15 | 2015-07-01 | 马玺渊 | A kind of volume relationship demonstration teaching aid |
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| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20160323 |
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| WD01 | Invention patent application deemed withdrawn after publication |