Volume of a figure

### 1.1. Knowledge to remember

**a) Example 1**

In the figure below, the cube is completely inside the rectangular box. We say: The volume of the smaller cube is greater than the volume of the rectangular box or the volume of the rectangular box is greater than the volume of the cube.

**b) Example 2**

Figure C consists of 4 identical cubes and Figure D also includes 4 similar cubes. We say: The volume of figure C is equal to the volume of figure D.

**c) Example 3**

Figure P consists of 6 identical cubes. We split the figure P into two shapes M, N: figure M consists of 4 cubes and figure N consists of 2 such cubes. We say: The volume of figure P is equal to the sum of the volumes of shapes M and N.

### 1.2. Solving textbook exercises page 115

**Lesson 1 of the textbook page 115:**

In the two pictures below:

Rectangular box A contains how many small cubes?

Cube B consists of how many small cubes?

Which figure has a larger volume?

**Solution guide:**

- Rectangular box A consists of 4 x 2 x 2 = 16 small cubes.
- Rectangular box B consists of 3 x 3 x 2 = 18 small cubes.

So figure B has a larger volume.

Lesson 2 Textbook page 115:

Figure A contains how many small cubes?

Figure B consists of how many small cubes?

Compare the volume of figure A and figure B.

*Solution guide:*

- Figure A has 5 x 3 x 3 = 45 small cubes.
- Figure B has 3 x 3 x 3 – 1 = 26 small cubes.

Which 45 > 26.

So the volume of figure A is larger than the volume of figure B.

Lesson 3 Textbook page 115:

There are 6 small cubes of side 1cm. Let’s arrange those 6 cubes into a rectangular box. How many different layouts are there?

*Solution guide:*

Because 6 = 1 x 6 = 2 x 3

So we have two ways to make a rectangle.

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