Topicmfd4332fb8484de3f_1528449000663_0Topic

Calculating the surface area and the volume of the cylindervolume of the cylindervolume of the cylinder.

Levelmfd4332fb8484de3f_1528449084556_0Level

Third

Core curriculummfd4332fb8484de3f_1528449076687_0Core curriculum

X. Solid geometry. The student:

4. recognizes an angle between segments and an angle between segments and planes in cylinders and cones (e.g. a line inclination angle, an angle between the slant height and the base of the cone) and works out the sizes of these angles;

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

Timingmfd4332fb8484de3f_1528449068082_0Timing

45 minutes

General objectivemfd4332fb8484de3f_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 objectivesmfd4332fb8484de3f_1528449552113_0Specific objectives

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

2. Calculating the surface area and volume of a cylindercylindercylinder using trigonometry

Learning outcomesmfd4332fb8484de3f_1528450430307_0Learning outcomes

The student:

1. Calculates the surface area and volume of a cylinder using trigonometry.

Methodsmfd4332fb8484de3f_1528449534267_0Methods

1. Open ear.

2. Situational analysis.

Forms of workmfd4332fb8484de3f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmfd4332fb8484de3f_1528450127855_0Introduction

The students work in pairs, using the „open ear” technique to recollect information about the cylindercylindercylinder and the formula for calculating the surface area and volume of the cylindervolume of the cylindervolume of the cylinder.

The teacher verifies their answers and explains any doubts.

Proceduremfd4332fb8484de3f_1528446435040_0Procedure

The teacher informs the student that the aim of the class is developing the ability to calculate the surface areas and volumes of the cylindercylindercylinder.

Working in groups, the students analyse the material shown in the multimedia presentation, paying special attention to the following stages of solving the task. They formulate hypotheses and conclusions.

[Slideshow]

The conclusion
In order to solve a task concerning calculating the surface areas and volumes of the cylindercylindercylinder, you need to do the following activities:

- make a diagram of the solid,
- find the given information and decide what information is needed to solve the task,
- list the formulae appropriate for the task,
- do the calculations,
- formulate your answer.

The students work individually to solve the tasks.

Task 1
The diagonal of the axial section of a cylindercylindercylinder has the length of 26 cm and forms angle α with the base of the cylinderbase of the cylinderbase of the cylinder so that $\cos \alpha =\frac{5}{13}$. Calculate the volume of the cylindervolume of the cylindervolume of the cylinder.

Answer: $600\mathrm{\pi }$ cmIndeks górny 3³.

Task 2
The curved surface of a cylindercylindercylinder equals $48\mathrm{\pi }$ dmIndeks górny 2² and the perimeter of its base equals $8\mathrm{\pi }{\mathrm{dm}}^{}$. Calculate the volume of the cylindervolume of the cylindervolume of the cylinder.

Answer: $96\mathrm{\pi }$ dmIndeks górny 3³.

Task 3
a. The radius of the base;

b. The altitude of the cylinderaltitude of the cylinderaltitude of the cylinder. were increased three times. How many times has the volume of the cylindervolume of the cylindervolume of the cylinder increased?

Answer: a) 9, b) 3.

Task 4
Daniela wants to paint 10 identical fence post. The posts have the shape of a cylinder whose altitude is 2 m and the diameter of the base is 10 cm. How many cans of paint must Daniela buy if you know that one can of paint is enough to paint 5 m2 of the surface?Task 4Daniela wants to paint 10 identical fence post. The posts have the shape of a cylinder whose altitude is 2 m and the diameter of the base is 10 cm. How many cans of paint must Daniela buy if you know that one can of paint is enough to paint 5 m2 of the surface?

Answer: 1 can.

Task 5
In a meadow there are 6 drainage ditches. Each ditch has a shape of a cylindercylindercylinder whose diameter is 30 cm and the length is 2 m. Calculate how many litres of water there are in the ditches. Give your calculation to the accuracy of 1 l.

Answer: 848 l.

Having solved all the tasks, the students present their results. The teacher assesses their work and explains the doubts.

An extra task:A drawer Has the length of 40 cm, the width 60 cm and the depth 15 cm. We put the maximum number of identical tins full of powdered chocolate into the drawer. Each tin has a shape of a cylinder with the altitude of 15 cm and the diameter of 10 cm. How big part of the drawer would be filled if the content of the tins was poured into the drawer?An extra taskAn extra task:A drawer Has the length of 40 cm, the width 60 cm and the depth 15 cm. We put the maximum number of identical tins full of powdered chocolate into the drawer. Each tin has a shape of a cylinder with the altitude of 15 cm and the diameter of 10 cm. How big part of the drawer would be filled if the content of the tins was poured into the drawer?

Answer: about 0,79.

Lesson summarymfd4332fb8484de3f_1528450119332_0Lesson summary

The students do the consolidation tasks. They cooperate to formulate the conclusions to memorize.

In order to solve a task concerning calculating the surface areas and volumes of the cylindercylindercylinder, you need to do the following activities:

- make a diagram of the solid,
- find the given information and decide what information is needed to solve the task,
- list the formulae appropriate for the task,
- do the calculations,
- formulate your answer.

Selected words and expressions used in the lesson plan

altitude of the cylinderaltitude of the cylinderaltitude of the cylinder

axial section of the cylinderaxial section of the cylinderaxial section of the cylinder

base of the cylinderbase of the cylinderbase of the cylinder

curved surface area of the cylindercurved surface area of the cylindercurved surface area of the cylinder

cylindercylindercylinder

diameter of the axial section of the cylinderdiameter of the axial section of the cylinderdiameter of the axial section of the cylinder

total surface area of the cylindertotal surface area of the cylindertotal surface area of the cylinder

volume of the cylindervolume of the cylindervolume of the cylinder