CN207571940U - A kind of volume verification demonstrating device - Google Patents
A kind of volume verification demonstrating device Download PDFInfo
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- CN207571940U CN207571940U CN201721245265.3U CN201721245265U CN207571940U CN 207571940 U CN207571940 U CN 207571940U CN 201721245265 U CN201721245265 U CN 201721245265U CN 207571940 U CN207571940 U CN 207571940U
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- hollow
- hollow ball
- ball
- cylinder
- cone
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Abstract
The utility model discloses a kind of volume verification demonstrating devices, include the combination container of built-in liquid, the combination container includes eight hollow ball A, a hollow ball B, a hollow cylinder and a hollow cone, eight hollow ball A are interconnected and are set on right over hollow ball B, the hollow cylinder is arranged side by side with hollow ball B, the hollow cylinder bottom surface is set in the same horizontal line with hollow ball B bottoms, and the hollow cone is just being erected on right over hollow cylinder.The utility model directly can intuitively recognize proportionate relationship, sphere volume calculation formula, cylinder and the circular cone volume relationship and circular cone cubature formula with verification sphere volume ratio and radius by demonstration.It is very useful during solid geometry teaching, one model can verify multiple formula, and the model for having elephant can more attract student's note that improving the interest and space imagining ability of student's learning mathematics knowledge, it is also beneficial to student's hands-on and memory, the mathematics core attainment of training student.
Description
Technical field
The utility model is related to a kind of maths demonstration laboratory apparatus, tool refers to a kind of volume verification demonstrating device.
Background technology
In mathematical studying, we will often calculate the volume of object, such as the volume of cuboid, the volume of square,
The volume of these objects can measure, and comparison for calculation methods is easily understood.The volume calculation formula of sphere is：V=4/3 π R3, circle
The cubature formula of cone is：V=1/3Sh=1/3 π R2The ratio between h, sphere volume is equal to the cube of the ratio between radius.From two dimension
Plane is transitioned into three dimensions, and student is needed to have an abstract three-dimensional thinking, beginner when comparing two sphere volumes easily with
Area ratio is obscured.Sphere volume is not talked about in teaching process with circular cone cubature formula yet and how to be derived, but is directly accused
It tells student and requires to remember, such teaching method is not easy to it is appreciated that sphere volume and circular cone cubature formula.The two are public
The derivation of formula is related to calculus principle.Provided that a kind of demonstration device can show the stereometer with verification sphere visual in imagely
Formula is calculated, volume proportionate relationship and the proportionate relationship of radius, the volume calculation formula of cone between sphere, this starts for student
Operation and memory are very useful.
Utility model content
In order to solve the above technical problems, technical solution provided by the utility model is：
A kind of volume verification demonstrating device includes the combination container of built-in liquid, and the liquid is coloured liquid, and the combination is held
Device includes eight hollow ball A, a hollow ball B, a hollow cylinder and a hollow cone, and eight hollow ball A are mutual
Connect and be set on right over hollow ball B, the hollow cylinder is arranged side by side with hollow ball B, the hollow cylinder bottom surface with it is hollow
Ball B bottoms are set in the same horizontal line, and the hollow cone is just being erected on right over hollow cylinder.Eight hollow ball A with
Hollow ball B is connected, and the hollow ball B is connected with hollow cylinder, and the hollow cylinder is connected with hollow cone, and described eight hollow
Ball A is equipped with valve with hollow ball B, hollow ball B and the junction of hollow cylinder, hollow cylinder and hollow cone.It is described hollow
The diameter of ball A is equal to the radius of hollow ball B, and the bottom surface radius of the hollow cylinder is equal to the radius of hollow ball B, the open circles
The height of column is equal to the radius of 4/3 times of hollow ball B, and the bottom surface radius and height of the hollow cone are respectively equal to the open circles
The bottom surface radius and height of column.Setting hollow ball A and hollow ball B is used to verify that the ratio between sphere volume is equal to the ratio between radius three times
Side；Setting hollow cylinder is to verify sphere cubature formula V=4/3 π r3；Hollow cone is set to hold by colored liquid in combination
Device various pieces shift, and to weigh container each section volume size, observer are allowed more intuitively to see different three-dimensional shape volumes
Between relationship.
As advanced optimizing, the hollow cylinder lateral wall is equipped with vertically trisection graduation mark, the sky
Bulbus cordis B lateral walls are equipped with and vertically halve graduation mark.Trisection graduation mark on the outside of hollow cylinder is convenient for intuitive reason
Solve the multiple proportion between circular cone volume and cylindrical volume.Bisection graduation mark on hollow ball B lateral walls causes in verification body
Product and the quantity that hollow ball A can be reduced during radius relationship.
As advanced optimizing for the technical program, the support platform is respectively fixed on hollow ball B bottoms, hollow cylinder
Bottom surface, hollow ball A tops, hollow cone top, hollow cylinder are far from hollow ball B sides and hollow cone far from hollow ball B mono-
Side.The setting of support platform makes volume verification demonstrating device that can balance ornaments along different directions when demonstrating different volumes relationship.
Volume verification demonstrating device provided by the utility model learnt area of a circle calculation formula, cylinder volume meter in student
After calculating formula, volume of cone calculation formula and sphere volume calculation formula, can directly intuitively it be recognized and tested by demonstration
Demonstrate,prove sphere volume ratio relationship, sphere volume calculation formula, cylinder and circular cone volume relationship and circular cone cubature formula.Three-dimensional several
Very useful in what teaching process, a model can verify multiple formula, and the model for having elephant can more attract the note of student
Meaning improves the interest and space imagining ability of student's learning mathematics knowledge, is also beneficial to student's hands-on and memory, and culture is learned
Raw mathematics core attainment.
Description of the drawings
Fig. 1 is a kind of structure diagram of volume verification demonstrating device embodiment of the utility model.
As shown in the figure：1st, liquid, 2, hollow ball A, 3, hollow ball B, 4, hollow cylinder, 5, hollow cone, 6, valve, 7, three
Evenly divided line, 8, halve graduation mark, 9, support platform.
Specific embodiment
The following describes the utility model in further detail with reference to the accompanying drawings.
In Fig. 1, a kind of volume verification demonstrating device includes the combination container of built-in liquid, and liquid 1 is colored liquid, is combined
Container includes eight hollow ball A2, a hollow ball B3, a hollow cylinder 4 and a hollow cone 5.Eight in the present embodiment
Hollow ball A2 forms two rows side by side two-by-two, and right over hollow ball B, and eight hollow ball A2 are interconnected, wherein two
A hollow ball A2 is connect with hollow ball B3 by carrying the conduit of valve 6.The present embodiment only enumerates eight hollow ball A2 of one kind
Arrangement mode, other should be regarded as equivalence transformation within the scope of protection of the utility model about the transformation of arrangement mode.
Hollow cylinder 4 is arranged side by side with hollow ball B3, and 4 bottom surface of hollow cylinder is located at same level with hollow ball B3 bottoms
On line, can intuitively it judge in the relatively height of hollow cylinder 4 and the size of the hollow radius of a ball, hollow cone 5 just erects
Right over hollow cylinder 4.Hollow ball B3 is connected with hollow cylinder 4 by carrying the conduit of valve 6, hollow cylinder 4 with it is hollow
Circular cone 5 is connected by carrying the conduit of valve 6.
For the ease of the intuitive judgment and verification of cubature formula, the diameter of hollow ball A2 is equal to the radius of hollow ball B3, empty
The bottom surface radius of heart cylinder 4 is equal to the radius of hollow ball B3, and the height of hollow cylinder 4 is equal to the radius of 4/3 times of hollow ball B3, empty
The bottom surface radius and height of heart circular cone 5 are respectively equal to the bottom surface radius and height of hollow cylinder 4.It is set on 4 lateral wall of hollow cylinder
There is vertically trisection graduation mark 7, hollow ball B3 lateral walls, which are equipped with, vertically halves graduation mark 8.
Support platform 9 is respectively fixed on hollow ball B3 bottoms, 4 bottom surface of hollow cylinder, hollow ball A2 tops, hollow cone 5
Top, hollow cylinder 4 are far from hollow ball B3 sides and hollow cone 5 far from hollow ball B3 sides.
When the volume verification demonstrating device is in original state, colored liquid 1 is filled in eight hollow ball A2, all valves
Door is closed.During demonstration, the valve 6 below hollow ball A2 is opened, when the colored liquid 1 of four hollow ball A2 flows into sky
When in bulbus cordis B3, metal line is just flushed with the bisection graduation mark 8 of hollow ball B3, when colored liquid 1 all flows into hollow ball
When in B3, entire hollow ball B3 is just filled, closes the valve 6 below hollow ball A2.It is possible thereby to it verifies, the ratio between sphere volume
Equal to the cube of the ratio between radius.Demonstration device is rotated by 90 ° counterclockwise, opens the valve between hollow ball B3 and hollow cylinder 4,
Colored liquid 1 is flowed into hollow cylinder 4, and fills entire hollow cylinder 4 completely, close hollow ball B3 and hollow cylinder 4 it
Between valve.The calculation formula of cylinder volume：V=Sh=π R24/3R, it is possible thereby to verify, sphere volume calculation formula V
=4/3 π R3.Demonstration device is rotated by 90 ° counterclockwise, opens the valve between hollow cylinder 4 and hollow cone 5, colored liquid 1
It flows into hollow cone 5, when filling, 4 liquid level graduation mark of hollow cylinder is at the first trisection graduation mark in top, thus may be used
With verification, the volume of circular cone is equal to 1/3rd of the contour cylindrical volume in bottom, the cubature formula V=1/3Sh of circular cone.
The utility model and embodiments thereof are described above, this description is no restricted, shown in attached drawing
Be also the utility model one of embodiment, practical structure is not limited thereto.All in all if this field
Those of ordinary skill is enlightened by it, without deviating from the purpose of the present invention, not inventively design with
The similar frame mode of the technical solution and embodiment, all should belong to the protection range of the utility model.
Claims (3)
1. a kind of volume verification demonstrating device, which is characterized in that include the combination container of built-in liquid, the liquid is coloured liquid
Body, the combination container include eight hollow ball A, a hollow ball B, a hollow cylinder and a hollow cone, described eight
A hollow ball A is interconnected and is set on right over hollow ball B, and the hollow cylinder is arranged side by side with hollow ball B, the open circles
Column bottom surface is set in the same horizontal line with hollow ball B bottoms, and the hollow cone is just being erected on right over hollow cylinder；
Eight hollow ball A are connected with hollow ball B, and the hollow ball B is connected with hollow cylinder, the hollow cylinder with it is hollow
Circular cone connects, the connection of eight hollow ball A and hollow ball B, hollow ball B and hollow cylinder, hollow cylinder and hollow cone
Place is equipped with valve；
The diameter of the hollow ball A is equal to the radius of hollow ball B, half of bottom surface radius equal to hollow ball B of the hollow cylinder
Diameter, the height of the hollow cylinder are equal to the radius of 4/3 times of hollow ball B, and the bottom surface radius and height of the hollow cone are respectively
Equal to the bottom surface radius and height of the hollow cylinder.
2. a kind of volume verification demonstrating device according to claim 1, which is characterized in that set on the hollow cylinder lateral wall
There is vertically trisection graduation mark, the hollow ball B lateral walls are equipped with and vertically halve graduation mark.
3. a kind of volume verification demonstrating device according to claim 2, which is characterized in that further include support platform, the branch
Support platform be respectively fixed on hollow ball B bottoms, hollow cylinder bottom surface, at the top of hollow ball A, at the top of hollow cone, hollow cylinder it is remote
From hollow ball B sides and hollow cone far from hollow ball B sides.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201721245265.3U CN207571940U (en) | 2017-09-27 | 2017-09-27 | A kind of volume verification demonstrating device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201721245265.3U CN207571940U (en) | 2017-09-27 | 2017-09-27 | A kind of volume verification demonstrating device |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN207571940U true CN207571940U (en) | 2018-07-03 |
Family
ID=62694650
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201721245265.3U Expired - Fee Related CN207571940U (en) | 2017-09-27 | 2017-09-27 | A kind of volume verification demonstrating device |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN207571940U (en) |
-
2017
- 2017-09-27 CN CN201721245265.3U patent/CN207571940U/en not_active Expired - Fee Related
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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 |
Granted publication date: 20180703 Termination date: 20190927 |
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| CF01 | Termination of patent right due to non-payment of annual fee |