Volume of rectangular box

### 1.1. Knowledge to remember

**a) Example: **Find the volume of a rectangular box with length 20cm, width 16cm and height 10cm.

To calculate the volume of the above rectangular box in cubic centimeters, we need to find the number of cubes 1cm^{3} Fill the box (see the drawings below).

After stacking 10 layers of 1cm . cube^{3} the box is just full.

Each layer has: 20 x 16 = 320 (1cm . cube^{3}).

10 layers have: 320 x 10 = 3200 (1cm . cube^{3}).

So the volume of the rectangular box is:

20 x 16 x 10 = 3200 (cm^{3})

**b) ***To calculate the volume of a rectangular box, we multiply the length by the width and then the height (same unit of measure).*.

Let V be the volume of the rectangular box, we have:

V = ax bxc

(a, b, c are the three dimensions of the rectangular box).

### 1.2. Solve textbook exercises page 121

**Lesson 1 Textbook page 121**

Find the volume of a rectangular box with length a, width b, height c

a) a = 5cm; b = 4cm; c = 9cm.

b) a = 1.5m; b = 1.1m; c = 0.5m.

c) a = \(\frac{2}{5}\)dm; b = \(\frac{1}{3}\)dm; c = \(\frac{3}{4}\)dm.

__Solution guide:__

a) The volume of the rectangular box is:

V = 5 x 4 x 9 = 180 (cm^{3})

b) The volume of the rectangular box is:

V = 1.5 x 1.1 x 0.5 = 0.825 (m^{3})

c) The volume of the rectangular box is:

\(V = \frac{1}{5} \times \frac{1}{3} \times \frac{3}{4} = \frac{1}{{10}}\left( {d{m) ^3}} \right)\)

Lesson 2 Textbook page 121

Calculate the volume of a block of wood of the form below:

__Solution guide:__

Divide the wooden block into two rectangular boxes A and B as shown below:

The width of rectangular box A is:

12 – 6 = 6 (cm)

The volume of rectangular box A is:

8 x 6 x 5 = 240 (cm^{3})

The volume of rectangle B is:

15 x 6 x 5 = 450 (cm^{3})

The volume of the wooden block is:

240 + 450 = 690 (cm^{3})

Answer: 690cm^{3}.

Lesson 3 Textbook page 121

Calculate the volume of the rock in the water tank according to the figure below:

__Solution guide:__

The volume of water in the tank is:

10 x 10 x 5 = 500 (cm^{3})

The total volume of the water and the rock is:

10 x 10 x 7 = 700 (cm^{3})

The volume of the rock is:

700 – 500 = 200 (cm^{3})

Answer: 200 (cm3)

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