Calculate Cube Edge Length: Given Face Area of 25 cm²

Shown below is a cube, the faces of which each equal 25 cm².

What are the lengths of the edges of the cube?

Video Solution

Solution Steps

00:00 Find the edge length of the cube

00:03 Let's mark the edges with A, all edges are equal in the cube:

00:06 Face area (square) equals the product of edges

00:09 Substitute appropriate values according to the given data and solve for the edge

00:12 Extract the root

00:15 Find the two possibilities for the edge

00:18 These are the two possibilities for the edge

00:24 The edge represents a length of a side, therefore must be positive

00:29 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 area of one face of the cube.
Step 2: Use the formula for the side length of a square face, $s = \sqrt{A}$ , where $A$ is the area.
Step 3: Calculate the side length.

Now, let's work through each step:

Step 1: The problem states that each face of the cube has an area of 25 cm².

Step 2: Since each face is a square, we use the formula $s = \sqrt{A}$ to find the side length, where $A = 25$ cm².

Step 3: Plugging in the value for $A$ , we get $s = \sqrt{25} = 5$ cm.

Therefore, the length of each edge of the cube is $5$ cm.