Topicmeda53df7bebb944a_1528449000663_0Topic

A cylindercylindercylinder. Surface area of the cylinder

Levelmeda53df7bebb944a_1528449084556_0Level

Third

Core curriculummeda53df7bebb944a_1528449076687_0Core curriculum

X. Solid Geometry (Stereometry). The student:

6) calculates the volume and surface area of prisms, pyramids, cylindercylindercylinder, cone and sphere, also with the use of trigonometry and theorems learned.

Timingmeda53df7bebb944a_1528449068082_0Timing

45 minutes

General objectivemeda53df7bebb944a_1528449523725_0General objective

Applying mathematical objects and manipulating them, interpreting mathematical concepts.

Specific objectivesmeda53df7bebb944a_1528449552113_0Specific objectives

1. Construction of the cylinder.

2. Calculation of the cylindercylindercylinder surface area.

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

Learning outcomesmeda53df7bebb944a_1528450430307_0Learning outcomes

The student:

- knows the construction of the cylindercylindercylinder,

- calculates cylinder surface area.

Methodsmeda53df7bebb944a_1528449534267_0Methods

1. Discussion.

2. Mind map.

Forms of workmeda53df7bebb944a_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmeda53df7bebb944a_1528450127855_0Introduction

The teacher informs the students that during the lesson they will determine the elements of the cylindercylindercylinder construction and calculate its surface area.

Proceduremeda53df7bebb944a_1528446435040_0Procedure

Discussion - What figure will we get by rotating a rectangle around a line containing one of its sides?

Work in groups.meda53df7bebb944a_1527752256679_0Work in groups.

Students create mind maps, on which they put information related to the cylinder, known from the elementary school. They mark the elements of the cylindercylindercylinder construction and its sections in the drawing.

Task
Students work individually using computers. Their task is to observe how the change of the height and radius of the cylinder basecylinder basecylinder base affect the dimensions of the figures forming the cylinder net.

[Geogebra applet]

Conclusions:

[Illustration 1]

- The surface area of the cylinder is equal to the net area of this cylinder.meda53df7bebb944a_1527752263647_0- The surface area of the cylinder is equal to the net area of this cylinder.

- The surface area P of the cylindercylindercylinder, with the height H and the radius of the base r, is equal:

where:
$P_p$ - the base area,
$P_b$ - lateral surface area.

Hence:

Students use the acquired knowledge to solve word problems.

Task
How many cmIndeks górny 2² of sheet were used to make a metal can in the shape of a cylindercylindercylinder with a height of 15 cm and a radius of 5 cm? Let’s assume $\mathrm{\pi }=\frac{22}{7}$.

Task
A square with a diagonal of 4 cm is rotated around a straight line with a square side. Specify the height, radius of the base of the resulting cylinder and calculate its surface area.

Task
The diagonal of the axial section of a cylindercylindercylinder has a length of 3 cm and forms with one of the sides of a rectangle, being an axial section of a cylinder, an angle of 30Indeks górny o^o. Calculate the total cylindercylindercylinder area.

Task
The axial section of the cylinder is a rectangle with the area 80 and the length 10. Calculate the base radius and the height of the cylindercylindercylinder. Consider two cases.

An extra task:
The lateral surface of the cylinder when unfolded on the plane is a rectangle with dimensions of 12 cm x 8 cm. Calculate the total cylindercylindercylinder area. Consider two cases.

Lesson summarymeda53df7bebb944a_1528450119332_0Lesson summary

Students do additional exercises.

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

- The cylinder is a figure that we get by rotating a rectangle around a line containing one of its sides.

- The surface area P of the cylinder, with the height H and the radius of the base r, is equal:

where:
$P_p$ - is the base area,
$P_b$ - is the lateral surface area.

Hence:

Selected words and expressions used in the lesson plan

cylindercylindercylinder

cylinder basecylinder basecylinder base

cylinder base radiuscylinder base radiuscylinder base radius

cylinder heightcylinder heightcylinder height

cylinder netcylinder netcylinder net

cylinder surface areacylinder surface areacylinder surface area

lateral surface area of a cylinderlateral surface area of a cylinderlateral surface area of a cylinder