Cube Properties: Analyzing the Relationship Between Faces and Surface Area

Look at the cube below.

Do all cubes have 6 faces, equaling its surface area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Does every cube have six faces that are equal in area?
00:10 Now, let's label each edge of the cube as A. All edges in a cube are the same length.
00:16 The area of each face, which is a square, is the product of side A times side A.
00:22 Since all edges are equal, this means all face areas are also equal.
00:29 And that's how we can confirm the answer to our question!

Step-by-step written solution

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1

Understand the problem

Look at the cube below.

Do all cubes have 6 faces, equaling its surface area?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the properties of a cube.
  • Step 2: Count the number of faces and relate to surface area.

Let's go through each step:
Step 1: A cube is a three-dimensional shape with all sides equal in length and each angle a right angle. A cube has 6 faces, each of which is a square.
Step 2: The surface area (A A ) of a cube is calculated as A=6s2 A = 6s^2 , where s s is the length of a side of the cube. The calculation considers contributions from all 6 faces, each being square, hence a cube having 6 faces is integral to the computation of its surface area. The number of faces is 6 and each is involved in computing the surface area through this formula.

Therefore, the statement that all cubes have 6 faces equating to the surface area property is Yes..

3

Final Answer

Yes.

Practice Quiz

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What are the dimensions of a cuboid composed of two 4X3 rectangles

and of four 4X4 squares?

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