Calculate Cube Edge Length from Face Area: 16 cm² Problem

Question

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

What is the length of the cube's edges?

Video Solution

Solution Steps

00:00 Find the length of the edge in the cube
00:03 We'll mark the edges with A, all edges are equal in the cube
00:06 The face area (square) equals the product of the edges
00:09 We'll substitute appropriate values according to the given data and solve to find the edge
00:12 Take the square root
00:15 We'll find the two possibilities for the edge
00:18 These are the two possibilities for the edge
00:23 The edge represents a length of a side, therefore must be positive
00:27 And this is the solution to the problem

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} .

Answer

4 4