104 LearnersLast updated on September 5, 2025
Volume of Hexagonal Pyramid
The volume of a hexagonal pyramid is the total space it occupies or the number of cubic units it can hold. A hexagonal pyramid is a 3D shape with a hexagonal base and triangular faces that meet at a common vertex. To find the volume of a hexagonal pyramid, we multiply the area of the base by the height of the pyramid and then divide by three. In real life, the volume of a hexagonal pyramid can relate to structures like certain types of tents or architectural designs. In this topic, let’s learn about the volume of a hexagonal pyramid.
What is the volume of a hexagonal pyramid?
The volume of a hexagonal pyramid is the amount of space it occupies. It is calculated by using the formula:
Volume = (Base Area x Height) / 3
Where ‘Base Area’ is the area of the hexagonal base, and 'Height' is the perpendicular distance from the base to the apex.
Volume of Hexagonal Pyramid Formula: To calculate its volume, you first find the area of the hexagonal base and then multiply it by the height of the pyramid, dividing the result by three.
The formula for the volume of a hexagonal pyramid is given as follows: Volume = (Base Area x Height) / 3
How to Derive the Volume of a Hexagonal Pyramid?
To derive the volume of a hexagonal pyramid, we use the concept of volume as the total space occupied by a 3D object.
The volume can be derived as follows: The formula for the volume of any pyramid is:
Volume = (Base Area x Height) / 3
For a hexagonal pyramid, calculate the area of the hexagonal base first and then divide the product of this base area and the height by three.
The volume of a hexagonal pyramid will be, Volume = (Base Area x Height) / 3
How to find the volume of a hexagonal pyramid?
The volume of a hexagonal pyramid is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). First, calculate the area of the hexagonal base, then use the height of the pyramid to find the volume.
Let’s take a look at the formula for finding the volume of a hexagonal pyramid:
1. Write down the formula Volume = (Base Area x Height) / 3
2. Calculate the base area, which is the area of the hexagon.
3. Use the height, which is the perpendicular distance from the base to the apex of the pyramid.
4. Substitute the values into the formula and solve.
Tips and Tricks for Calculating the Volume of a Hexagonal Pyramid
Remember the formula: The formula for the volume of a hexagonal pyramid is: Volume = (Base Area x Height) / 3
Break it down: Calculate the area of the hexagonal base first. This can often be done using the formula for the area of a regular hexagon: (3√3/2) x side² if the side length is known.
Simplify the numbers: Make sure to simplify the fractions and make calculations step by step to avoid errors.
Check for height: Ensure you use the perpendicular height from the base to the apex, not the slant height.
Common Mistakes and How to Avoid Them in Volume of Hexagonal Pyramid
Making mistakes while learning the volume of a hexagonal pyramid is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of hexagonal pyramids.
Volume of Hexagonal Pyramid Examples
Problem 1
A hexagonal pyramid has a base area of 24 cm² and a height of 10 cm. What is its volume?
The volume of the hexagonal pyramid is 80 cm³.
Explanation
To find the volume of a hexagonal pyramid, use the formula: V = (Base Area x Height) / 3 Here, the base area is 24 cm², and the height is 10 cm, so: V = (24 x 10) / 3 = 240 / 3 = 80 cm³
Problem 2
A hexagonal pyramid has a base area of 36 m² and a height of 15 m. Find its volume.
The volume of the hexagonal pyramid is 180 m³.
Explanation
To find the volume of a hexagonal pyramid, use the formula: V = (Base Area x Height) / 3 Substitute the base area (36 m²) and height (15 m): V = (36 x 15) / 3 = 540 / 3 = 180 m³
Problem 3
The volume of a hexagonal pyramid is 90 cm³. If the base area is 18 cm², what is the height of the pyramid?
The height of the hexagonal pyramid is 15 cm.
Explanation
If you know the volume and base area and need to find the height, rearrange the formula: Height = (Volume x 3) / Base Area Height = (90 x 3) / 18 = 270 / 18 = 15 cm
Problem 4
A hexagonal pyramid has a base area of 50 inches² and a height of 12 inches. Find its volume.
The volume of the hexagonal pyramid is 200 inches³.
Explanation
Using the formula for volume: V = (Base Area x Height) / 3 Substitute the base area (50 inches²) and height (12 inches): V = (50 x 12) / 3 = 600 / 3 = 200 inches³
Problem 5
A hexagonal pyramid has a base area of 72 ft² and a height of 9 ft. How much space (in cubic feet) does it occupy?
The hexagonal pyramid has a volume of 216 cubic feet.
Explanation
Using the formula for volume: V = (Base Area x Height) / 3 Substitute the base area (72 ft²) and height (9 ft): V = (72 x 9) / 3 = 648 / 3 = 216 ft³
FAQs on Volume of Hexagonal Pyramid
1.Is the volume of a hexagonal pyramid the same as the surface area?
2.How do you find the volume if the base area and height are given?
3.What if I have the volume and need to find the height?
4.Can the base area or height be a decimal or fraction?
5.What is the difference between the slant height and the height of a hexagonal pyramid?
Important Glossaries for Volume of Hexagonal Pyramid
- Base Area: The area of the hexagonal base of the pyramid.
- Height: The perpendicular distance from the base to the apex of the pyramid.
- Volume: The amount of space enclosed within a 3D object, calculated as (Base Area x Height) / 3 for a hexagonal pyramid.
- Cubic Units: The units of measurement used for volume (e.g., cm³, m³).
- Slant Height: The distance along the triangular face from the base to the apex, not used in volume calculation.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
