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Understanding the Surface Area and Volume of Cubes: Perfect Cubes and Their Formulas, Lecture notes of Analytical Geometry and Calculus
A detailed explanation of the surface area and volume of cubes, including the concept of perfect cubes and their formulas. It covers various edge lengths and calculates the corresponding surface areas and volumes. Useful for students in mathematics and physics.
What you will learn
- What is the relationship between the edge length and the surface area of a cube?
- How do you calculate the volume of a cube?
- How does the edge length affect the surface area and volume of a cube?
- What are some traditional units of volume and how do they relate to cubic centimeters?
- What are perfect cubes and how are they related to the volume and surface area of a cube?
Typology: Lecture notes
2021/2022
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This is a square centimeter (cm
2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0° 1 2 3 4 5
This is a cubic centimeter (cm
3
This is a cubic centimeter (cm
3
Each edge has a length of 1 cm.
A cubic centimeter has six faces that
each have an area of 1 cm
2
This is a cubic centimeter (cm
3
Each edge has a length of 1 cm.
A cubic centimeter has six faces that
each have an area of 1 cm
2
The total surface area is
6 • 1 cm
2
= 6 cm
2
Each edge of this cube has a length of 2 cm. Each of the six faces has an area of 4 cm 2 .
Each edge of this cube has a length of 2 cm. Each of the six faces has an area of 4 cm 2 . The total surface area is 6 • 4 cm 2 = 24 cm 2 .
Each edge of this cube has a length of 3 cm. Each of the six faces has an area of 9 cm 2 .
Each edge of this cube has a length of 3 cm. Each of the six faces has an area of 9 cm 2 . The total surface area is 6 • 9 cm 2 = 54 cm 2 .
Each edge of this cube has a length of 4 cm. Each of the six faces has an area of 16 cm 2 .
Each edge of this cube has a length of 4 cm. Each of the six faces has an area of 16 cm 2 . The total surface area is 6 • 16 cm 2 = 96 cm 2 .
The volume of a 3 - dimensional figure is the space inside the figure.
The volume of a 3 - dimensional figure is the space inside the figure. 1 cm 3
The volume of a 3 - dimensional figure is the space inside the figure. 1 cm 3 8 cm 3 27 cm 3
The volume of a 3 - dimensional figure is the space inside the figure. 1 cm 3 8 cm 3 27 cm 3 64 cm 3