Cubic meters

### 1.1. Knowledge to remember

**a) Cubic meter**

To measure volume, people also use cubic meters.

Cubic meter is the volume of a cube with side length 1m.

Cubic meter is abbreviated as m^{3} .

– A cube with side 1m consists of 1000 cubes with side 1dm.

We have: 1m^{3} = 1000dm^{3}

1m^{3} = 1 000 000 cm^{3} (= 100 x 100 x 100)

**b) Comments:**

– Each unit of volume measurement is 1000 times larger than the next smaller unit.

– Each unit of volume is equal to \(\frac{1}{{1000}}\) the next larger unit.

square meter^{3} |
dm^{3} |
cm^{3} |

1m = 1000dm |
1dm = 1000cm = \(\frac{1}{{1000}}\)m |
1cm =\(\frac{1}{{1000}}\)dm |

### 1.2. Solution of textbook exercises on page 118

**Lesson 1 Textbook page 118**

a) Read the following measurements:

15m^{3}; 205m^{3} ; \(\frac{{25}}{{100}}{m^3}\); 0.911m^{3}

b) Write down the volume measurements:

Seven thousand two hundred cubic meters;

Four hundred cubic meters;

One-eighth of a cubic meter;

Zero point zero five cubic meters.

*Solution guide:*

a)

15m^{3} : Fifteen cubic meters.

205m3 : Two hundred and five cubic meters.

\(\frac{{25}}{{100}}{m^3}\): Twenty-five percent of a cubic meter.

0.911m^{3} : No point nine hundred and eleven cubic meters.

b)

Seven thousand two hundred cubic meters: 7200cm^{3}

Four hundred cubic meters 400cm^{3}

One-eighth of a cubic meter:\(\frac{{1}}{{8}}{m^3}\)

Zero point zero five cubic meters: 0.05m^{3}

Lesson 2 Textbook page 118

a) Write the following measurements as cubic decimeters:

1cm^{3}; 5.216m^{3}; 13.8m^{3}; 0.22m^{3}

b) Write the following measurements as cubic centimeters:

1dm^{3}; 1,969dm^{3}; \(\frac{1}{4}\) m^{3}; 19.54 m^{3}.

*Solution guide:*

a)

1cm^{3} = \(\frac{1}{{1000}}\)dm^{3} = 0.001dm^{3}

5.216m^{3} = 5.216 x 1000dm^{3} = 5216dm^{3}

13.8m^{3} = 13.8 x 1000dm^{3} =13800dm^{3}

0.22m^{3} = 0.22 x 1000dm^{3} = 220dm^{3}

b)

1dm^{3} = 1000cm^{3}

1,969dm^{3} = 1,969 x 1000cm^{3} = 1969cm^{3}

\(\frac{1}{4}\)m^{3} = \(\frac{1}{4}\) x 1 000 000cm^{3} = 250 000cm^{3}

19.54m^{3} = 19.54 x 1 000 000cm^{3} = 19 540 000cm^{3}

Lesson 3 Textbook page 118

People make a rectangular box out of cardboard. Assume that the box has length 5dm, width 3dm and height 2dm. How many 1dm cubes can be arranged?^{3} to fill that box?

*Solution guide:*

After filling the box, we get 2 layers of 1dm . cubes^{3}.

Each layer has the number of cubes 1dm^{3} was:

5 × 3 = 15 (picture)

The number of 1dm3 cubes to fill the box is:

15 × 2 = 30 (picture)

Answer: 30 pictures.

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