Rozwiązywanie zadań  – prostopadłościan

Learning objectives

You will develop competences in communicating in English, as well as mathematical and basic competences in science, technology and IT, and you will develop learning skills.

You will use the properties of a cuboid in geometric and practical problems.

You will develop skills in calculating the surface area and volume of a cuboid.

Learning effect

• You will learn to use the properties of a cuboid in geometric and practical problems.

• You will learn how to solve word problems in which you will calculate the surface area and volume of a cuboid.

Review what you remember about cuboids.

The aim of the lesson will be to develop and systematize knowledge and skills related to the cuboids. Defeat the obstacles by solving the word problems. If you solve the task correctly - you score 1 point. If you make a mistake you score (-1) point.

High in the mountains Geometric Dragon lives alone. The dragon promised the prize to anyone who visited it. The uphill road is not easy. Different obstacles are awaiting the visitors. Try to overcome these obstacles and win the prize.

Obstacle 1

What is it:

• it is similar to a shoesbox,

• it is similar to a book,

• it is an interesting object,  

• it has four faces and two bases?

Obstacle 2

Draw any cuboidcuboidcuboid. Use the computer and applet now.

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Aplet geogebra: Prostopadłościan. Poniżej znajduje się galeria będąca wersją alternatywną dla aplikacji.

Aplet geogebra: Prostopadłościan. Poniżej znajduje się galeria będąca wersją alternatywną dla aplikacji.

Zasób interaktywny dostępny pod adresem https://zpe.gov.pl/a/D5Lx5vSOf

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Rysunek prostopadłościanu. Wierzchołki prostopadłościanu oznaczone są wielkimi literami: podstawa dolna – A ,B, C, D, podstawa górna – E, F, G, H.

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Rysunek prostopadłościanu. Wierzchołki prostopadłościanu oznaczone są wielkimi literami: podstawa dolna – A ,B, C, D, podstawa górna – E, F, G, H. Zamalowane są płaszczyzny podstaw.

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Rysunek prostopadłościanu. Wierzchołki prostopadłościanu oznaczone są wielkimi literami: podstawa dolna – A ,B, C, D, podstawa górna – E, F, G, H. Zaznaczone są krawędzie podstaw prostopadłościanu.

Mark on your drawing all the cuboidcuboidcuboid parts, mentioned in the applet. Give properties to these elements. Check the correctness of the solution every time.

Obstacle 3

Geometric Dragon always eats a rectangular cubecubecube of butter with dimensions of 2 dm by 3 dm by 4 dm for breakfast. Calculate the volumevolumevolume of this cube.

Obstacle 4

Geometric Dragon lives in the summer in Palace A, while in winter - in Palace B. Both palaces are built of identical cubic elements. The dragon wants to cover the palace roofs with a gold sheet and the walls - with the silver one.

• Which roof needs more metal?

• Which palace needs less metal to cover its walls?

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Rysunek dwóch różnych brył złożonych z sześciu jednakowych sześcianów. Każda z brył ułożona jest w dwóch rzędach, sześciany w drugim rzędzie zawsze leżą bezpośrednio na sześcianie z pierwszego rzędu . Pierwsza podpisana jest Palace A, druga Palace B. Palace A w dolnym rzędzie ma 5 sześcianów, a w drugim 1. Palace B w dolnym rzędzie ma 4 sześciany, a w drugim 2.

Obstacle 5

In front of you there is a ditch, which contains 120 l of water. The ditch has a rectangular shape with a length of 0.5 m and a width of 0.4 m. Calculate the depth of this ditch.

Obstacle 6

There is an aquarium on the side of the road. Goldfish swim in it. The aquarium has the shape of a cubecubecube with an edgeedge edge length of 2 m.

The dragon claims that the diagonaldiagonaldiagonal of the face of this cube is shorter than 400 cm. Justify that he is right.

Obstacle 7 - the last and the most difficult one:

The dragon stores his hats in a box of 80000 cmIndeks górny 3³. The basebasebase of this box is a square with a surface areasurface areasurface area of 16 dmIndeks górny 2². How much carton was used to make this box?

If you received more than 4 points for solving the tasks, you have overcome all obstacles. You can visit the Geometric Dragon and win the prize.
Which tasks were the most difficult to solve and why.

In geometrical tasks, careful attention should be paid to the fact that all quantities used in a given calculation are presented in the same units.

Remember:

In geometrical tasks, pay careful attention to the fact that all the quantities used in a given calculation are presented in the same units.

Do the revision exercises.

Exercises

Glossary

Keywords

basebasebase

cubecube cube

cuboidcuboidcuboid

surface areasurface areasurface area

volumevolumevolume