Finding the Volume of a Cube: Formula and Tasks

In this publication, we will look at how you can find the volume of a cube and analyze examples of solving problems to fix the material.

The formula for calculating the volume of a cube

1. Through the length of the rib

The volume (V) of a cube is equal to the product of its length times its width times its height. Because the given values ​​of the cube are equal, therefore, its volume is equal to the cube of any edge.

V = a ⋅ a ⋅ a = a³

2. Through the length of the diagonal of the face

As we know, the faces of a cube are equal to each other and are a square, the side of which can be found through the length of the diagonal using the formula: a=d/√2.

Therefore, the volume of a cube can be calculated as follows:

Examples of tasks

Task 1

Calculate the volume of a cube if its edge is 5 cm.

Decision:

We substitute the given value into the formula and get:

V = 5 cm ⋅ 5 cm ⋅ 5 cm = 125 cm³.

Task 2

It is known that the volume of a cube is 512 cm³. Find the length of its edge.

Decision:

Let the edge of the cube be a. We derive its length from the volume calculation formula:

Task 3

The diagonal length of a cube face is 12 cm. Find the volume of the figure.

Decision:

Apply the formula that uses the diagonal of the face: