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
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- 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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Abstract
本发明公开了一种球体锥体圆柱体体积关系验证仪，包括内置液体的组合容器和支架，组合容器包括空心圆锥、空心球、空心圆柱、第一连接管、第二连接管；空心圆锥底面朝上倒立设于空心球正上方，空心圆柱设于空心球正下方，空心圆锥顶端和空心球顶部通过第一连接管连接，空心球底部、空心圆柱顶面中部通过第二连接管连接；空心圆锥底面直径和高度相等，等于空心圆柱底面直径和高度，等于空心球直径；液体总体积等于空心圆锥体积；第一连接管和第二连接管上分别设有第一电磁阀和第二电磁阀，支架上设有电磁阀控制器。本发明可用于几何数学演示实验，有利于提高课堂教学效果，还能取代传统沙漏用于计时。
The invention discloses an instrument for verifying the relationship between volumes of spheres, cones, and cylinders, which includes a combined container with built-in liquid and a bracket. The combined container includes a hollow cone, a hollow sphere, a hollow cylinder, a first connecting pipe, and a second connecting pipe; the bottom surface of the hollow cone Upside-down is set directly above the hollow sphere, and the hollow cylinder is set directly below the hollow sphere. The top of the hollow cone and the top of the hollow sphere are connected by the first connecting pipe, and the bottom of the hollow sphere and the middle of the top surface of the hollow cylinder are connected by the second connecting pipe; The diameter and height of the bottom surface of the cone are equal, equal to the diameter and height of the bottom surface of the hollow cylinder, and equal to the diameter of the hollow sphere; the total volume of the liquid is equal to the volume of the hollow cone; the first connecting pipe and the second connecting pipe are respectively provided with a first solenoid valve and a second solenoid valve , There is a solenoid valve controller on the bracket. The invention can be used in geometric and mathematics demonstration experiments, is beneficial to improving classroom teaching effects, and can also replace traditional hourglasses for timing.
Description
技术领域technical field
本发明涉及一种数学演示实验仪器，具体为一种球体锥体圆柱体体积关系验证仪。The invention relates to a mathematical demonstration experiment instrument, in particular to a volume relation verification instrument for spheres, cones, cylinders.
背景技术Background technique
球体、圆锥体、圆柱体的体积公式及证明是初等几何教学的一个难点。在等底等高的情况下，圆锥体的体积是圆柱体体积的三分之一，而球的体积则是以其大圆为底、直径为高的圆柱体体积的三分之二。如能通过实验方法验证上述关系，则由上述三种几何体中任意一个的体积计算公式可推得其它两个的体积公式，同时能变抽象为形象，增加学生的学习兴趣。目前，缺乏一种既方便携带和课堂演示、又能快速验证球体、圆锥体、圆柱体体积关系的数学演示实验仪器。The volume formulas and proofs of spheres, cones, and cylinders are a difficult point in elementary geometry teaching. With the same base and height, the volume of the cone is one-third of the volume of the cylinder, and the volume of the sphere is two-thirds of the volume of the cylinder with its great circle as its base and its diameter as its height. If the above relationship can be verified by experimental methods, the volume calculation formula of any one of the above three geometric bodies can be used to deduce the volume formulas of the other two. At the same time, abstraction can be transformed into images to increase students' interest in learning. At present, there is a lack of a mathematical demonstration experimental instrument that is not only convenient for carrying and classroom demonstration, but also can quickly verify the relationship between the volumes of spheres, cones, and cylinders.
发明内容Contents of the invention
本发明的目的，是开发一种用于几何数学演示实验的球体锥体圆柱体体积关系验证仪。The purpose of the present invention is to develop a sphere-cone-cylinder-volume relationship verification instrument for geometric mathematics demonstration experiments.
为了解决上述技术问题，本发明采用以下技术方案：In order to solve the above technical problems, the present invention adopts the following technical solutions:
一种球体锥体圆柱体体积关系验证仪，包括内置液体的组合容器和固定于组合容器外用于保护组合容器的支架，所述组合容器包括空心圆锥、空心球、空心圆柱、第一连接管、第二连接管；空心圆锥底面朝上倒立设于空心球正上方，空心圆柱设于空心球正下方，空心圆锥顶端和空心球顶部均开有小孔并通过第一连接管连接，空心球底部、空心圆柱顶面中部均开有小孔并通过第二连接管连接；所述空心圆锥的底面直径和高度相等，等于空心圆柱底面直径和高度，等于空心球的直径；为方便观察，所述液体为有色液体，其总体积等于空心圆锥的体积；所述第一连接管和第二连接管上分别设有控制第一连接管和第二连接管管路通断的第一电磁阀和第二电磁阀，支架上设有控制第一电磁阀和第二电磁阀的电磁阀控制器，电磁阀控制器与第一电磁阀和第二电磁阀电相连。A sphere-cone-cylindrical volume relationship verifier, comprising a combined container with built-in liquid and a bracket fixed outside the combined container for protecting the combined container, the combined container includes a hollow cone, a hollow sphere, a hollow cylinder, a first connecting pipe, The second connecting pipe; the bottom of the hollow cone is upside down and placed directly above the hollow ball, the hollow cylinder is arranged directly below the hollow ball, the top of the hollow cone and the top of the hollow ball are provided with small holes and are connected by the first connecting pipe, the bottom of the hollow ball 1. The middle part of the top surface of the hollow cylinder has a small hole and is connected by a second connecting pipe; the diameter and height of the bottom surface of the hollow cone are equal, equal to the diameter and height of the bottom surface of the hollow cylinder, and equal to the diameter of the hollow sphere; for the convenience of observation, the The liquid is a colored liquid, and its total volume is equal to the volume of the hollow cone; the first connecting pipe and the second connecting pipe are respectively provided with a first solenoid valve and a second connecting pipe to control the opening and closing of the first connecting pipe and the second connecting pipe. Two solenoid valves, a solenoid valve controller for controlling the first solenoid valve and the second solenoid valve is arranged on the bracket, and the solenoid valve controller is electrically connected with the first solenoid valve and the second solenoid valve.
所述支架上还设有用于读取空心圆锥、空心球、空心圆柱几何尺寸以及液面位置的长度标尺。The bracket is also provided with a length scale for reading the geometric dimensions of the hollow cone, hollow sphere, hollow cylinder and the position of the liquid level.
开始实验前，液体全部位于空心圆锥内，第一电磁阀和第二电磁阀处于闭合状态。按下电磁阀控制器开关，打开第一电磁阀开通第一连接管，液体流向空心球。当液体全部流入空心球时，正好装满半个空心球。接着电磁阀控制器打开第二电磁阀开通第二连接管，液体流向空心圆柱。当液体全部流入空心圆柱时，液面正好位于空心圆柱高度的三分之一位置。由此通过实验，验证上述圆锥体、球体、圆柱体的体积关系，并可利用圆柱体的体积计算公式推出球体和圆锥体的体积公式。Before starting the experiment, all the liquid is located in the hollow cone, and the first solenoid valve and the second solenoid valve are in a closed state. Press the electromagnetic valve controller switch, open the first electromagnetic valve and open the first connecting pipe, and the liquid flows to the hollow ball. When the liquid all flows into the hollow ball, it just fills up half of the hollow ball. Then the electromagnetic valve controller opens the second electromagnetic valve to open the second connecting pipe, and the liquid flows to the hollow cylinder. When all the liquid flows into the hollow cylinder, the liquid level is just at one-third of the height of the hollow cylinder. Therefore, through experiments, the volume relationship of the above-mentioned cone, sphere, and cylinder is verified, and the volume formula of the sphere and the cone can be deduced by using the volume calculation formula of the cylinder.
本发明由于采用上述设计，既方便教师携带，又能快速验证球体、圆锥体、圆柱体体积关系，可用于几何数学演示实验，有利于提高课堂教学效果。本发明还能取代传统沙漏用于计时，利用液体从圆锥体流入球体和从球体流入圆柱体的时间不同，形成双时段计时功能。Due to the adoption of the above-mentioned design, the present invention is not only convenient for teachers to carry, but also can quickly verify the relationship between the volumes of spheres, cones, and cylinders. The invention can also replace the traditional hourglass for timekeeping, and utilizes the difference in time when the liquid flows from the cone into the sphere and from the sphere into the cylinder to form a dual-period timekeeping function.
附图说明Description of drawings
下面结合附图对本发明作进一步说明。The present invention will be further described below in conjunction with accompanying drawing.
图1是本发明的构成示意图(液体全部位于圆锥体内时)。Fig. 1 is a schematic diagram of the composition of the present invention (when all the liquids are located in the cone).
图2是验证锥体球体体积关系示意图(液体全部位于球体内时)。Fig. 2 is a schematic diagram of verifying the relationship between the volume of the cone and the sphere (when all the liquid is inside the sphere).
图3是验证球体圆柱体体积关系示意图(液体全部位于圆柱体内时)。Fig. 3 is a schematic diagram for verifying the relationship between the volume of a sphere and a cylinder (when all the liquid is in the cylinder).
图中：1.空心圆锥，2.空心球，3.空心圆柱，4.第一连接管，5.第二连接管，6.液体，7.支架，41.第一电磁阀，45.电磁阀控制器，51.第二电磁阀，71.长度标尺。In the figure: 1. Hollow cone, 2. Hollow ball, 3. Hollow cylinder, 4. First connecting pipe, 5. Second connecting pipe, 6. Liquid, 7. Bracket, 41. First solenoid valve, 45. Electromagnetic Valve controller, 51. Second solenoid valve, 71. Length scale.
具体实施方式detailed description
如图1所示，本发明包括内置液体6的组合容器和固定于组合容器外用于保护组合容器的支架7，组合容器包括空心圆锥1、空心球2、空心圆柱3、第一连接管4、第二连接管5，空心圆锥1底面朝上倒立设于空心球2正上方，空心圆柱3设于空心球2正下方，空心圆锥1顶端和空心球2顶部均开有小孔并通过第一连接管4连接，空心球2底部、空心圆柱3顶面中部均开有小孔并通过第二连接管5连接。空心圆锥1的底面直径和高度相等，等于空心圆柱3的底面直径和高度，等于空心球2的直径。为方便观察，液体6为有色液体，其总体积等于空心圆锥1的体积。第一连接管4和第二连接管5上分别设有控制第一连接管4和第二连接管5管路通断的第一电磁阀41和第二电磁阀51，支架上设有控制第一电磁阀41和第二电磁阀51的电磁阀控制器45，电磁阀控制器45与第一电磁阀41和第二电磁阀51电相连。As shown in Figure 1, the present invention comprises the combination container of built-in liquid 6 and is fixed on the support 7 that is used to protect combination container outside the combination container, and combination container comprises hollow cone 1, hollow ball 2, hollow cylinder 3, first connecting pipe 4, The second connection pipe 5, the bottom of the hollow cone 1 is turned upside down and placed directly above the hollow ball 2, the hollow cylinder 3 is located directly below the hollow ball 2, the top of the hollow cone 1 and the top of the hollow ball 2 have small holes and pass through the first The connecting pipe 4 is connected, and the bottom of the hollow ball 2 and the middle part of the top surface of the hollow cylinder 3 are all provided with small holes and are connected by the second connecting pipe 5 . The bottom diameter and height of the hollow cone 1 are equal, equal to the bottom diameter and height of the hollow cylinder 3, and equal to the diameter of the hollow sphere 2. For the convenience of observation, the liquid 6 is a colored liquid, and its total volume is equal to the volume of the hollow cone 1 . The first connecting pipe 4 and the second connecting pipe 5 are respectively provided with a first solenoid valve 41 and a second solenoid valve 51 for controlling the on-off of the first connecting pipe 4 and the second connecting pipe 5 , and the bracket is provided with a control first solenoid valve. A solenoid valve controller 45 for the solenoid valve 41 and the second solenoid valve 51 , the solenoid valve controller 45 is electrically connected with the first solenoid valve 41 and the second solenoid valve 51 .
支架7上还设有用于读取空心圆锥1、空心球2、空心圆柱3几何尺寸以及液面位置的长度标尺71。The support 7 is also provided with a length scale 71 for reading the geometric dimensions of the hollow cone 1, the hollow sphere 2, the hollow cylinder 3 and the position of the liquid level.
如图2所示，原位于空心圆锥1内的液体全部流入空心球2内，此时液体6正好装满空心球2体积的一半。As shown in Figure 2, the liquid originally located in the hollow cone 1 all flows into the hollow sphere 2, and the liquid 6 just fills half of the volume of the hollow sphere 2 at this moment.
如图3所示，液体6全部流入空心圆柱3内，此时液面正好位于空心圆柱3高度的三分之一位置处。As shown in FIG. 3 , all the liquid 6 flows into the hollow cylinder 3 , and the liquid level is just at one-third of the height of the hollow cylinder 3 at this moment.
Claims (2)
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| Application Number | Priority Date | Filing Date | Title |
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| CN201610005728.2A CN105427714A (en) | 2016-01-05 | 2016-01-05 | Instrument for verifying volume relations among sphere, cone and cylinder |
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| CN201610005728.2A CN105427714A (en) | 2016-01-05 | 2016-01-05 | Instrument for verifying volume relations among sphere, cone and cylinder |
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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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Application publication date: 20160323 |