Calculate Cube Surface Area: Finding Total Area from 6 cm² Faces

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

• Step 1: Determine the length of a side of the cube.
• Step 2: Calculate the total surface area of the cube using the determined side length.

Let's work through each step:

Step 1: Determine the length of a side of the cube.
The area of one face of the cube is given as 6 cm². Since the face of a cube is a square, we can use the formula for the area of a square, which is $a^2$, where $a$ is the side length of the square. Therefore, we have:

$a^2 = 6$

To find $a$, take the square root of both sides:

$a = \sqrt{6}$

Step 2: Calculate the total surface area of the cube.
The formula for the surface area $S$ of a cube with side length $a$ is given by:

$S = 6a^2$

Substitute the value of $a^2$ from Step 1:

$S = 6 \times 6 = 36$

Therefore, the surface area of the cube is $36 \text{ cm}^2$.