Cube Volume Formula: Verifying V = edge³ in Three-Dimensional Geometry

Look at the cube below.

Is the volume of a cube equal to the length of the edges cubed?

Video Solution

Solution Steps

00:00 Is the cube's volume equal to the edge length cubed?

00:03 We'll use the formula for calculating volume

00:07 Width times length times height

00:11 In a cube, all edges are equal

00:16 Let's substitute the edge lengths into the formula and calculate the volume

00:22 We can see that the cube's volume equals the edge length cubed

00:27 And this is the solution to the question

Step-by-Step Solution

To determine whether the volume of a cube is equal to the length of the edges cubed, we follow these steps:

Step 1: Recognize that a cube is a three-dimensional shape with six equal square faces. All edges of a cube are of equal length.
Step 2: Recall the formula for the volume of a cube, given by $V = s^3$ , where $s$ is the length of one of the cube's edges.
Step 3: The question asks if the volume is equal to the edge length cubed. We note that the formula $V = s^3$ clearly indicates that the volume of a cube is indeed calculated by cubing the length of its edges.

Thus, the volume of a cube is $\mathbf{equal}$ to the length of the edges cubed.

Therefore, the correct answer to this problem is:

Yes