Topicm732424b00b87ed97_1528449000663_0Topic

Volume of the conevolume of the coneVolume of the cone

Levelm732424b00b87ed97_1528449084556_0Level

Third

Core curriculumm732424b00b87ed97_1528449076687_0Core curriculum

X. Solid geometry (Stereometry). The student:

1) calculates the volume and surface area of prisms, pyramids, cylinders, cones, balls, also using trigonometry and the theorems learned.

Timingm732424b00b87ed97_1528449068082_0Timing

45 minutes

General objectivem732424b00b87ed97_1528449523725_0General objective

Applying mathematical objects and manipulating them, interpreting mathematical concepts.

Specific objectivesm732424b00b87ed97_1528449552113_0Specific objectives

1. Calculation of the volume of the conevolume of the conevolume of the cone.

2. Communicating in English, developing competences in mathematics, science, technology and IT, developing learning skills.

Learning outcomesm732424b00b87ed97_1528450430307_0Learning outcomes

The student:

- calculates the volume of the conevolume of the conevolume of the cone.

Methodsm732424b00b87ed97_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm732424b00b87ed97_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionm732424b00b87ed97_1528450127855_0Introduction

The teacher informs the students that during the lesson they will calculate the volume of the conevolume of the conevolume of the cone.

Procedurem732424b00b87ed97_1528446435040_0Procedure

Task
Students work individually using computers. Their task is to observe the ratio of volume of the cylinder to the volume of the conevolume of the conevolume of the cone with the same base and the same height.

On the basis of this observations, students formulate a formula for the volume of the coneconecone.

[Geogebra applet]

- Formula for the volume of the cone.
The $V$ volume of the cone with the base radius $r$ and the height $H$ is expressed by the formula:m732424b00b87ed97_1527752263647_0- Formula for the volume of the cone.
The $V$ volume of the cone with the base radius $r$ and the height $H$ is expressed by the formula:

Students use the acquired knowledge in the word problems.

Task
Calculate the volume of the conevolume of the conevolume of the cone, whose height is equal to 5 cm, and the radius of its base is equal to 8 cm.

Task
The figure shows axial sections of the cones.

[Illustration 1]

Calculate the volume for each of these ones.

Task
A rectangular trapezoid with a base length of 10 cm and 6 cm and a longer arm length of 3 cm is given. Calculate the volume of the solid that will be created as a result of the rotation of this trapezoid around the longer base.

Task
The paper cup in the shape of a coneconecone has a height of 15 cm and a base radiusbase radiusbase radius of 6 cm, and the paper cup in the shape of a cylinder has a height of 15 cm and a radius of 4 cm. Which cup can fit more drink?

Task for volunteers
The height of an equilateral triangle which is an axial section of the coneconecone is equal to $\sqrt{2}$. Calculate the area and volume of this coneconecone.

Lesson summarym732424b00b87ed97_1528450119332_0Lesson summary

Students do additional exercises.

Then, they summarize the lesson together, formulating the formula to remember.

- The $V$ volume of the coneconecone with the base radiusbase radiusbase radius $r$ and the height $H$ is expressed by the formula:

Selected words and expressions used in the lesson plan

base radiusbase radiusbase radius

coneconecone

cone basecone basecone base

cone heightcone heightcone height

net of the conenet of the conenet of the cone

surface area of the conesurface area of the conesurface area of the cone

volume of the conevolume of the conevolume of the cone