Calculate Cube Side Length from Surface Area: 24 cm² Problem

Question

The surface area of a cube is 24 cm².

How long are the sides of the cube?

00:00 Find the cube's edge

00:04 A cube is made up of squares, therefore all edges are equal

00:09 The surface area of the cube equals the area of 6 faces

00:25 Let's substitute appropriate values and solve for edge A

00:28 Let's isolate A

00:45 And this is the solution to the question

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

Now, let's work through each step:

Step 1: We know the total surface area of the cube is given as 24 cm².

Step 2: The formula for the surface area of a cube is:

$S = 6a^2$

where $S$ is the surface area and $a$ is the side length of the cube.

Step 3: We set the surface area equal to 24 cm² and solve for $a$ :

$6a^2 = 24$

Divide both sides by 6:

$a^2 = 4$

Take the square root of both sides to solve for $a$ :

$a = \sqrt{4} = 2 \text{ cm}$

Therefore, the length of each side of the cube is $2 \, \text{cm}$ .