Topicmc08e9869ed795a93_1528449000663_0Topic

The volume of the prism

Levelmc08e9869ed795a93_1528449084556_0Level

Second

Core curriculummc08e9869ed795a93_1528449076687_0Core curriculum

XI. Solid geometry. The student:

1) recognizes prisms and pyramids – including right regular and regular;

2) calculates the volumes and the surface area of right regular and regular prisms and also the ones that are not right at the level of difficulty not higher than the example task: The base of the right regular prism is an isosceles triangle, whose two equal angles are 45° each, and the longest side has the length of $6\sqrt{2}$ dm. One of the sides of a rectangle, which is the face with the largest area, is 4 dm long. Calculate the volume and the total surface area of this prism.

Timingmc08e9869ed795a93_1528449068082_0Timing

45 minutes

General objectivemc08e9869ed795a93_1528449523725_0General objective

Using simple, well‑known mathematical objects, interpretation of mathematical concepts and operating mathematical objects.

Specific objectivesmc08e9869ed795a93_1528449552113_0Specific objectives

1. Calculating the volume of the prism.

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

Learning outcomesmc08e9869ed795a93_1528450430307_0Learning outcomes

The student:

- calculates the volume of the prism.

Methodsmc08e9869ed795a93_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workmc08e9869ed795a93_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc08e9869ed795a93_1528450127855_0Introduction

The teacher informs the students that during this class they will calculate the volume of the prism.

Proceduremc08e9869ed795a93_1528446435040_0Procedure

Task

The students work individually, using their computer. Their task is to observe how to calculate the volume of the prism.

[Geogebra applet]

Geogebra calculator rounds results and in some cases results are approximate.

The conclusion:

- The volume of the prism is expressed with formula:

where:
PIndeks dolny p_p – the base area,
h – the altitude of the prism.

The students use the information to solve the tasks.

Task

[Illustration 1]

The base of the prism in the picture below is a trapezoid. The altitude of the prism equals 16 cm. Calculate its volume.

Task

How many litres of water can you put into aquarium, whose shape is the regular quadrangular prism? The base length is 40 cm and the altitude is 35 cm.mc08e9869ed795a93_1527752263647_0How many litres of water can you put into aquarium, whose shape is the regular quadrangular prism? The base length is 40 cm and the altitude is 35 cm.

Task

All the edges of the regular prism are the same length. Calculate the volume of this prism knowing that its base is:
a) a triangle with the side of 4 cm,
b) a hexagon with the side of 6 cm.mc08e9869ed795a93_1527752256679_0All the edges of the regular prism are the same length. Calculate the volume of this prism knowing that its base is:
a) a triangle with the side of 4 cm,
b) a hexagon with the side of 6 cm.

Task

The lateral surface area of the regular quadrangular prism equals 48. Calculate its volume if the altitude of the prism is 3 cm.mc08e9869ed795a93_1527712094602_0The lateral surface area of the regular quadrangular prism equals 48. Calculate its volume if the altitude of the prism is 3 cm.

Task

The regular quadrangular prism, whose base edge is 4 cm and the altitude 10 cm, was cut by a plane going through parallel diagonals of the top and bottom base. Calculate the volume of this prism, the length of its diagonal and the surface area of the section.

Lesson summarymc08e9869ed795a93_1528450119332_0Lesson summary

The students do additional tasks.

Next, they summarize the class and formulate the conclusions that they need to remember.

- The volume of the prism is expressed with formula:

where:
PIndeks dolny p_p – the base area,
h – the altitude of the prism.

Selected words and expressions used in the lesson plan

the base area of the prismthe base area of the prismthe base area of the prism

the prismthe prismthe prism

the total surface area of the prismthe total surface area of the prismthe total surface area of the prism

the volume of the prismthe volume of the prismthe volume of the prism