Volume of a cube

### 1.1. Knowledge to remember

**a) Example**

If the cube has sides 3cm, the volume is:

V = 3 x 3 x 3 = 27 (cm^{3})

**b)** *To calculate the volume of a cube, multiply the side by the side and then multiply by the side*.

If a cube has side a, then the volume V is:

V = axaxa

### 1.2. Solve textbook exercises on pages 122, 123

**Lesson 1 Textbook page 122**

Write the appropriate measurement in the blank:

Cube | (first) | (2) | (3) | (4) |

Side length | 1.5m | \(\frac{5}{8}dm\) | ||

Area of one side | 36cm^{2} |
|||

Total area | 600dm^{2} |
|||

Volume |

__Solution guide:__

+) Cubes (1) and (2) students calculate by themselves.

+) Cube (3):

Since 36=6×6, the side of the cube is 6cm long.

The total area is: 36×6=216(cm^{2})

The volume of the cube is: 6×6×6=216(cm^{3})

+) Cube (4):

The area of a face is: 600:6=100(dm^{2})

Since 100=10×10, the side of the cube is 10dm long.

The volume of the cube is: 10×10×10=1000(dm^{3})

We have the following result:

Cube | (first) | (2) | (3) | (4) |

Side length | 1.5m | \(\frac{5}{8}dm\) | 6cm | 10dm |

Area of one side | 2.25m2 | \(\frac{{25}}{{64}}\)dm2 | 36cm2 | 100dm^{2} |

Total area | 13.5m2 | \(\frac{{75}}{{32}}\)dm2 | 216cm2 | 600dm2 |

Volume | 3,375m3 | \(\frac{{125}}{{512}}\)dm3 | 216cm3 | 1000dm^{3} |

Lesson 2 Textbook page 122

A metal cube has a side of 0.75m. Each cubic decimeter of that metal weighs 15kg. How many kilograms does that metal block weigh?

__Solution guide:__

The volume of that metal block is:

0.75 x 0.75 x 0.75 = 0.421875 (m^{3})

We have: 0.421875 m^{3}= 421,875dm^{3}

The mass of metal that weighs in kilograms is:

15 x 421.875 = 6328,125 (kg)

Answer: 6328,125kg.

Lesson 3 Textbook page 123

A rectangular box is 8cm long, 7cm wide and 9cm high. A cube has sides equal to the average of the three dimensions of the above rectangular box. Calculate:

a) The volume of the rectangular box;

b) The volume of the cube.

__Solution guide:__

a) The volume of the rectangular box is:

8×7×9=504 (cm^{3})

b) The length of the side of the cube is:

(8+7+9):3=8(cm)

The volume of the cuboid is:

8×8×8=512 (cm^{3})

Answer: a) 504cm^{3};

b) 512cm^{3}

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