How to calculate the volume of a HEXAHEDRON

To calculate the volume of a regular hexahedron you need to know the measurements of the width, length and height. The formula used to calculate it is the following: V = L x W x H. At unProfesor we tell you.

Hexahedrons are polyhedra that are made up of six faces, these being polygons that have five or fewer sides. In a new lesson from a Teacher we will see how to calculate the volume of a hexahedron. We will start with the concept of hexahedron, its elements and then we will see the types of hexahedrons that exist. We will finish by calculating its volume. To consolidate the content we will do some examples and an exercise.

Index

1. What is a hexahedron?
2. How to calculate the volume of a hexahedron: formula and example
3. Example of how to calculate the volume of a hexahedron
4. Characteristics of hexahedrons and elements
5. 4 types of hexahedrons
6. Exercise and solution

In geometry, when we talk about hexahedron we refer to a polyhedron that is formed by

A hexahedron is then, a three dimensional figure which is formed from several polygons that can be the same or different. These polygons can be quadrilaterals, triangles, and pentagons.

When a hexahedron is made up of six equal squares, it is a polyhedron. regular, and it's called Cube. Any hexahedron formed by faces that are equal to each other will be a regular polyhedron.

To calculate the volume of a regular hexahedron, also called a cube, you need to know the measurements of the width, length and height.

The formula used to calculate it is the following:

V = L x W x H

Being

• V: volume
• L: long
• A: width
• H: high

Example

Once these values ​​are known, the volume of a cube can be calculated very easily. So let's look at an example.

If I want to calculate the volume of a regular hexahedron that is 6 meters long, 5 meters wide and 4 meters high, then we solve by substituting the values ​​where appropriate in the formula.

• V = L x W x H
• V = 6 x 5 x 4
• V = 120

The total volume of the cube is 120 cubic meters.

So that you understand how to calculate the volume of a hexahedron, here we leave you 2 clear and concise examples.

Example 1

We want to calculate the total volume of a cube that is 30 cm long, 25 cm wide and 40 cm high.

Solution.

• V = L x W x H
• V = 30 x 25 x 40
• V = 30,000

The total volume of the cube is 30,000 cubic centimeters.

Example 2

The total volume of a cube is 141,750 cubic centimeters. If its length is 45 centimeters and its width is 50 centimeters, how high is its height?

• V = L x W x H
• 141,750 = 45 x 50 x H
• 141,750 / 45 / 50 = H
• 63 = H

The height of the cube is 63 centimeters.

The characteristics of hexahedrons are the following:

• convex polyhedron: any segment or line that joins two of the points of the hexahedron is contained within it.
• They have six faces.
• Faces are made up of figures that only have five sides or less.
• They are solids belonging to space
• Their faces can be the same or different geometric figures.

Elements of a hexahedron

The elements of a hexahedron are the following:

• Faces: The faces are the polygons that form a hexahedron, that is, its sides.
• Edges: The edges are the unions between the faces of a hexahedron.
• Vertices: The vertices are the points where the edges of the hexahedron meet.
• Dihedral angle: It is the angle formed when two faces of the hexahedron are joined.
• polyhedron angle: is the angle formed from the sides that coincide at a vertex.

The types of hexahedrons The best known are the following.

Rectangular prism

A rectangular prism is a hexahedron in which the bases are rectangles and the four faces are quadrilaterals. It has six faces that have four sides each, eight are its vertices and twelve are its edges.

pentagonal pyramid

A pentagonal pyramid is a hexahedron that is formed by a pentagon as a base and its five faces are triangles. It has six faces that have five sides for its base and three sides for its faces, ten are its edges and six are its vertices.

Double tetrahedron

A double tetrahedron is a hexahedron that is formed by two joined pyramids whose bases are triangular. It has six faces that have three sides each, five are its vertices and nine are its edges.

Cube

A cube is a hexahedron that is made up of six equal faces that are squares. It is known as a Platonic solid. It has six identical faces that have four sides each, eight are its vertices and twelve are its edges.

We finish this lesson on calculating the volume of a hexahedron, with an exercise with solutions so you can practice at home.

Statement

The total volume of a cube is 384.8 cubic meters. If its height is 8 meters and its width is 6.5 meters, how long is its length?

Solution

• V = L x W x H
• 384.8 = L x 8 x 6.5
• 384.8 / 8 / 6.5 = L
• 7.4 = L

The length of the cube is 7.4 meters.

If you want to read more articles similar to How to calculate the volume of a hexahedron, we recommend that you enter our category of Geometry.