Topicma2a48ed1ba8bcf58_1528449000663_0Topic

The sections of the ballballball, the surface area of the ballsurface area of the ballsurface area of the ball

Levelma2a48ed1ba8bcf58_1528449084556_0Level

Third

Core curriculumma2a48ed1ba8bcf58_1528449076687_0Core curriculum

X. Solid geometry. The student:

6. calculates the volume and the surface areasurface areasurface area of a prism, pyramid, cylinder, cone, sphere using trigonometry and theorems.

Timingma2a48ed1ba8bcf58_1528449068082_0Timing

45 minutes

General objectivema2a48ed1ba8bcf58_1528449523725_0General objective

Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

Specific objectivesma2a48ed1ba8bcf58_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Getting to know the sections of the ballballball.

3. Calculating the surface area of the ballsurface area of the ballsurface area of the ball.

Learning outcomesma2a48ed1ba8bcf58_1528450430307_0Learning outcomes

The student:

- gets to know the sections of the ballballball,

- calculates the surface area of the ballsurface area of the ballsurface area of the ball.

Methodsma2a48ed1ba8bcf58_1528449534267_0Methods

1. Mind map.

2. Situation analysis.

Forms of workma2a48ed1ba8bcf58_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionma2a48ed1ba8bcf58_1528450127855_0Introduction

Working in pairs, the students prepare mind maps containing all the information about the ballballball that they have already acquired. They pay special attention to the definition of the ball, the sphere and the elements of the ball.

Then, they present their posters. The teacher verifies the information and explains doubts.

Procedurema2a48ed1ba8bcf58_1528446435040_0Procedure

The students recollect the information about the ballballball – the method of obtaining the ball and its elements.

The teacher informs the students that the aim of the class is calculating the surface area of the ballsurface area of the ballsurface area of the ball and getting to know the sections of the ball.

The students work individually guessing what shape a section of the ballballball has. They formulate hypotheses and compare them with appropriate models. They formulate the conclusion.

Conclusion:

Any cross section of the ball is a circle.ma2a48ed1ba8bcf58_1527752263647_0Any cross section of the ball is a circle.

The teacher informs the students that the section of the ball which passes through the centre of the ball is called the great circle of the ballgreat circle of the ballgreat circle of the ball.

[Illustration 1]

The students use the information to do the task together.

Task
The radius of the ballradius of the ballradius of the ball equals 20 cm. The cross sectioncross sectioncross section of the ballballball was drawn 12 cm away from the great circle of the ballgreat circle of the ballgreat circle of the ball. Calculate the circumference of this section.

Students work in groups analysing the Slideshow presenting the formula for the surface area of the ballsurface area of the ballsurface area of the ball. They write down the formula.

[Slideshow]

The formula for the surface area of the ball:

$P=4·\mathrm{\pi }·{\mathrm{R}}^2$

P - the surface area of the ball,
R - the radius of the ball.ma2a48ed1ba8bcf58_1527752256679_0The formula for the surface area of the ball:

$P=4·\mathrm{\pi }·{\mathrm{R}}^2$

P - the surface area of the ball,
R - the radius of the ball.

The students work in pairs looking for the relation between the surface area of the great circlecirclecircle and the surface area of the ball. They formulate the conclusion.

Conclusion:

The surface area of the ballsurface area of the ballsurface area of the ball is four times bigger than the surface areasurface areasurface area of the great circle.

The students use the information to do the tasks individually.

Task
A part of the ballballball, whose radiusradiusradius is 8 cm, was cut off 5 cm away from the centre of the ball. Calculate the ratio of the section to the area of the great circle of the ballgreat circle of the ballgreat circle of the ball.

Task
The circle, whose diameterdiameterdiameter is $2\sqrt{2}$ cm, was cut into four identical parts. One of these sectors of the circlecirclecircle was revolved around its radiusradiusradius. Calculate the surface areasurface areasurface area of the obtained solid.

Task
Two parallel planes cut a ballballball and form two sections, whose surface areas equal $9·\mathrm{\pi }$ and $36·\mathrm{\pi }$ respectively. The distance between the planes is 9. Calculate the surface area of the ballsurface area of the ballsurface area of the ball.

Task
The ratio of the surface areas of two balls is 4, and the difference between their radii is 15 cm. Calculate the radii of these balls.

Task
The ratio of the diameters of two balls is 6 : 5. What is the ratio of the surface areasurface areasurface area of these balls? Justify your answer.

An extra task
Let’s make an assumption that the Earth is a ballballball and the length of the equator is 40 000 000 m. We surrounded the Earth along the equator with a band measuring 40 000 100 m. What is the distance between the band and the surface of the Earth?

Lesson summaryma2a48ed1ba8bcf58_1528450119332_0Lesson summary

The students do the consolidation tasks.

They formulate the conclusions to be remembered:

- Any cross section of the ball is a circle.
- The surface area of the ball is four times bigger than the surface area of the great circle.ma2a48ed1ba8bcf58_1527712094602_0- Any cross section of the ball is a circle.
- The surface area of the ball is four times bigger than the surface area of the great circle.

Selected words and expressions used in the lesson plan

ballballball

circlecirclecircle

cross sectioncross sectioncross section

diameterdiameterdiameter

great circle of the ballgreat circle of the ballgreat circle of the ball

hemispherehemispherehemisphere

radiusradiusradius

radius of the ballradius of the ballradius of the ball

surface areasurface areasurface area

surface area of the ballsurface area of the ballsurface area of the ball