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?
- 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.
- 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?
Because 6 = 1 x 6 = 2 x 3
So we have two ways to make a rectangle.