Calculate Cube Edge Length from Face Area: 16 cm² Problem

The area of each face of the cube is 16 cm².

What is the length of the cube's edges?

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Step-by-step video solution

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00:08 Let's find the length of one edge in this cube.
00:11 We'll call each edge A. In a cube, all edges are equal.
00:16 The area of one face is calculated by multiplying two edges.
00:21 Now, use the given data to substitute and solve for edge A.
00:26 Take the square root to find A.
00:29 This gives us two possible values for A.
00:32 Remember, since A is a length, it has to be positive.
00:36 And that's how we solve this problem!

Step-by-step written solution

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1

Understand the problem

The area of each face of the cube is 16 cm².

What is the length of the cube's edges?

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Step-by-step solution

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

  • Step 1: Identify the given information.
  • Step 2: Apply the formula for the area of a square to find the edge length.
  • Step 3: Solve for the side length of the square face of the cube.

Now, let's work through each step:
Step 1: We know that each face of the cube has an area of 16 cm².
Step 2: The formula for the area of a square is A=side2 A = \text{side}^2 .
Step 3: We need to solve for the side length, so rearrange the formula: side=A\text{side} = \sqrt{A}. Given A=16 A = 16 , we find the side length: side=16=4\text{side} = \sqrt{16} = 4 cm.

Therefore, the solution to the problem is the length of the cube’s edges is 4 cm \text{the length of the cube's edges is } 4 \text{ cm} .

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Final Answer

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A cube has a total of 14 edges.

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