Topicm7923a71b2125f5b7_1528449000663_0Topic

Volume of the ballvolume of the ballVolume of the ball

Levelm7923a71b2125f5b7_1528449084556_0Level

Third

Core curriculumm7923a71b2125f5b7_1528449076687_0Core curriculum

X. Solid geometry (Stereometry). Student:

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

Timingm7923a71b2125f5b7_1528449068082_0Timing

45 minutes

General objectivem7923a71b2125f5b7_1528449523725_0General objective

Applying mathematical objects and manipulating them, interpreting mathematical concepts.

Specific objectivesm7923a71b2125f5b7_1528449552113_0Specific objectives

1) Calculation of the volume of the ballballball

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

Learning outcomesm7923a71b2125f5b7_1528450430307_0Learning outcomes

The student:

- calculates the volume of the ballvolume of the ballvolume of the ball

Methodsm7923a71b2125f5b7_1528449534267_0Methods

1) Discussion.

2) Case study.

Forms of workm7923a71b2125f5b7_1528449514617_0Forms of work

1) Group work.

2) Whole class work.

LESSON STAGES

Introductionm7923a71b2125f5b7_1528450127855_0Introduction

The teacher points out a student to remind the whole class all he or she knows about the ballballball.

The teacher informs students that during the lesson they will calculate the volume of the ballvolume of the ballvolume of the ball.

Procedurem7923a71b2125f5b7_1528446435040_0Procedure

Students work individually using computers. Their task is to observe what solid is formed as a result of the rotation of the semicircle around the straight line on which its diameter lies.

[Geogebra applet]

Group work
Each group receives from the teacher an empty ball‑shaped container and several identical containers in the shape of cone filled with sand. The radius of the base of the cone‑shaped vessel is equal to the height of the vessel and at the same time is equal to the radius of the empty ball‑shaped container.

Students pour sand from consecutive cone‑shaped containers into a ball‑shaped container. They check how many containers they poured sand from.

Students’ conclusions
A ball‑shaped container fits all the sand from four cone‑shaped containers. Thus, the volume of the ball‑shaped vessel is four times the volume of a cone‑shaped vessel.m7923a71b2125f5b7_1527752263647_0A ball‑shaped container fits all the sand from four cone‑shaped containers. Thus, the volume of the ball‑shaped vessel is four times the volume of a cone‑shaped vessel.

Conclusion
The V volume of the ball with the radius r is equal to $V=\frac{4}{3}\pi r^3$.m7923a71b2125f5b7_1527752256679_0The V volume of the ball with the radius r is equal to $V=\frac{4}{3}\pi r^3$.

Students use the acquired knowledge to solve word problems.

Task
Calculate the volume of the ballvolume of the ballvolume of the ball with a diameter of $3\sqrt{2}$.

Task
A spherespheresphere with a radius of 3 cm was inserted into a water‑filled cube‑shaped container with an edge of 8 cm. How many cmIndeks górny 3³ of water remained in the container? Round the result to the 2 decimal places.

Task
Calculate the surface area of the ballballball whose volume is equal to $972\pi$.

Task
The ballballball with the radius of 4 and the cylinder with the radius of the base 5 have equal volumes. Calculate the height of the cylinder.

Task for volunteers
A ball‑shaped candle with a radius of 5 cm, melted into a cone‑shaped candle with the same radius of the base as the radius of the ballradius of the ballradius of the ball. What is the height of the cone?

Lesson summarym7923a71b2125f5b7_1528450119332_0Lesson summary

Students do additional exercises.
Then they summarize the lesson together, formulating the conclusions to remember.

The V volume of the ballvolume of the ballvolume of the ball with the radius r is equal to $V=\frac{4}{3}\pi r^3$.

Selected words and expressions used in the lesson plan

ballballball

centre of the ballcentre of the ballcentre of the ball

great diskgreat diskgreat disk

radius of the ballradius of the ballradius of the ball

spherespheresphere

volume of the ballvolume of the ballvolume of the ball