Volume of Hexagonal Prism

The volume of a hexagonal prism is the space occupied by it. A prism is a three-dimensional shape having identical bases, flat rectangular side faces, and the same cross-section all along its length. Prisms are classified into different types and named as per the shape of their base. A hexagonal prism, as the name says, is a three-dimensional solid that has two hexagonal bases, bottom, and top. The side faces of a hexagonal prism are rectangular in shape. There is a formula to find the volume of a hexagonal prism. Let's explore and learn in detail!

The volume of the hexagonal prism is defined as the capacity of the hexagonal prism. In geometry, a hexagonal prism is a three-dimensional shape with two hexagonal bases and six rectangular faces. A hexagonal prism is a polyhedron with 8 faces, 18 edges, and 12 vertices where out of the 8 faces, 6 faces are in the shape of rectangles and 2 faces are in the shape of hexagons. The top and bottom of the hexagonal prism are shaped as a hexagon and are congruent to each other. On one hand, its long diagonals always cross the center point of the hexagon and on the other hand, its short diagonals do not cross the center point. The volume of the hexagonal prism is measured in cubic units such as cm³, m³, in³, etc.

We will see the formulas to calculate the volumes of different types of hexagonal prisms. The volume of any prism can be obtained by finding the product of its base area and its height. i.e., the volume of a prism = base area × height. We will use this formula to calculate the volume of a hexagonal prism as well. We know that the base of a hexagonal prism is a hexagon. By applying the above formula to a hexagonal prism. Thus, the volume of a hexagonal prism = area of base × height.

The volume of a hexagonal prism determines the capacity of the prism. As per the general formula of the volume of a prism, that is, volume = area of base × height, the formula for the volume of hexagonal prism = area of the hexagonal face x-height of the prism. The area of a regular hexagon with base length a is [(3√3)/2]a² and height is h. Thus, the formula for the volume of a hexagonal prism is: Volume =area of base × height = [(3√3)/2]a²h cubic units where

• a is the base length
• h is the height of the prism

We can also use the formula V = 3abh, where

• a = apothem length
• b = length of a side of the base
• h = height of the prism.

There are 2 different types of hexagonal prisms i.e. regular hexagonal prisms and irregular hexagonal prisms.

• A regular hexagonal prism is a prism with bases shaped like a hexagon with all the sides of the same length. The angles of the regular hexagonal prism are also the same.
• An irregular hexagonal prism is a prism where all the sides of a hexagonal base do not have the same lengths. The angles are also not the same.

Here are the steps to calculate the volume of a (regular) hexagonal prism. We need to be sure that all measurements are of the same units.

• Step 1: Identify the base edge a and find the base area of the prism using the formula a².
• Step 2: Identify the height of the given hexagonal prism.
• Step 3: Put the respective values in the formula, v = [(3√3)/2]a²h
• Step 4: Write the value of the volume of the hexagonal prism so obtained with appropriate cubic units.

Now refer to the example given below for more clarity.

Example: Calculate the volume of the hexagonal prism with a base edge of 4 feet and a height of 8 feet.

Solution: Given that base edge, a = 4 feet and height, h = 8 feet. The volume of the hexagonal prism is obtained using the formula V =base area × height or [(3√3)/2]a²h. The steps to determine the volume of the hexagonal prism are:

• Step 1: The area of the base of the hexagonal prism is found using the formula, [(3√3)/2]a² = [(3√3)/2](4)²= 41.568 square feet.
• Step 2: The height of the prism is 8 ft.
• Step 3: The volume of the hexagonal prism = base area × height = 332.544 × 8 = 332.544cubic feet.

Thus, the volume of the hexagonal prism is 332.544 cubic feet.

Related Topics

Listed below are a few interesting topics related to the volume of hexagonal prism, take a look.

• Volume of Hexagonal Cylinder
• Surface Area of Hexagonal Prism
• Hexagonal Pyramid

What Is the Volume of Hexagonal Prism?

The volume of the hexagonal prism refers to the capacity of the hexagonal prism. It is the product of the base area and the height of the prism. It is measured in cubic units.

What Is the Formula To Find the Volume of Hexagonal Prism?

The formula for the volume of a hexagonal prism is, volume = [(3√3)/2]a²h cubic units where a is the base length and h is the height of the prism. We can also use the other formula V = 3abh, where a = apothem length, b = length of a side of the base, and h = height of the prism.

How To Find the Volume of a Hexagonal Prism With Base Area and Height?

Since the volume of any prism can be obtained by multiplying its base area by its height, we can use this formula to calculate the volume of a hexagonal prism as well. Knowing that the base of a hexagonal prism is a hexagon, just apply the above formula to a hexagonal prism. Therefore, the volume of a hexagonal prism = area of base × height.

How To Find the Volume of an Oblique Hexagonal Prism?

In any oblique prism, the bases are not aligned to each other. Also, the lateral faces are parallelograms. Just like the volume of any other prism, the volume of an oblique prism can be found as the product of the area of the base and the height. Here, height is the perpendicular distance between the two bases.

How To Calculate the Volume of a Hexagonal Prism?

To calculate the volume of a hexagonal prism, follow the steps given below:

• Step 1: Find the base area using the appropriate formula.
• Step 2: Check for the height of the given hexagonal prism.
• Step 3: Put the values of the dimensions in the formula, v = [(3√3)/2]a²h
• Step 4: Write the final value with appropriate cubic units.

What Happens To the Volume of the Hexagonal Prism If Its Height Is Doubled?

We know that the formula for the volume of the hexagonal prism is v = 3abh. If its height gets doubled, the height will become 2h, then the volume of the new hexagonal prism will be 3ab(2h) = 2(3abh) = 2v. Thus, we can say that the volume will also get doubled.

What Happens To the Volume of the Hexagonal Prism If Its Base Length Is Doubled and Height Is Reduced To Half?

The formula for the volume of the hexagonal prism is v = 3abh. If its base length gets doubled, the new base becomes 2b, and the new height will be reduced to half, the new height will become h/2. Then the volume of the new hexagonal prism will be 3a(2b)(h/2) = 3abh = v. Thus, we can say that the volume will remain the same.