Rectangular box, cube
1.1. Knowledge to remember
Matchboxes and bricks are rectangular in shape.
A rectangular box has 6 faces (as shown in the figure): two bottom faces (face 1 and face 2) and four sides (face 3, face 4, face 5 and face 6) are rectangles. Side 1 and side 2; side 3 and side 5; side 4 and side 6.
The rectangular box (right image) has:
– The vertex centers are: vertex A, vertex B, vertex C, vertex D, vertex M, vertex N, vertex P, vertex Q.
– The twelve edges are: side AB, edge BC, edge DC, edge AD, edge MN, edge NP, edge QP, edge MQ, edge AM, edge BN, edge CP, edge DQ.
The rectangular box has three dimensions: length, width, and height.
We also often encounter in practice some objects such as dice having the shape of a cube.
A cube has six faces that are equal squares,
1.2. Solve textbook exercises page 108
Lesson 1 Textbook page 108
Write the correct number in the blank:
Based on the theory of rectangular boxes and cubes, we have the following results:
Lesson 2 Textbook page 108
a) Show the equal sides of the rectangular box (right figure).
b) Know that a rectangular box has length 6cm, width 3cm, height 4cm. Calculate the area of the bottom surface of MNPQ and the side faces ABNM, BCPN.
a) The equal sides of the rectangular box are:
AB = CD = MN = PQ
AD = BC = MQ = NP
AM = BN = CP = DQ
b) The area of the bottom surface of MNPQ is:
6 x 3 = 18 (cm2)
The area of the side surface ABNM is:
6 x 4 = 24 (cm2)
The area of the side surface BCPN is:
4 x 3 = 12 (cm2)
Answer: b) MNPQ bottom surface: 18cm2
ABNM bottom surface: 24cm2
BCPN bottom: 12cm2
Lesson 3 Textbook page 108
Which of the following figures is a rectangular box and which is a cube?
- Figure A is a rectangular box (because there are three dimensions: length, width, height).
- Figure B is neither a rectangle nor a cube.
- Figure C is a cube (because there are 6 faces that are all equal squares).