103 LearnersLast updated on July 20th, 2025
Volume of Rectangular Pyramid
The volume of a rectangular pyramid is the total space it occupies or the number of cubic units it can hold. A rectangular pyramid is a 3D shape with a rectangular base and four triangular faces. To find the volume of a rectangular pyramid, we multiply the area of the base by the height and then divide by three. In real life, kids relate to the volume of a rectangular pyramid by thinking of things like a tent, a teepee, or a pyramid. In this topic, let’s learn about the volume of a rectangular pyramid.
What is the volume of the rectangular pyramid?
The volume of a rectangular pyramid is the amount of space it occupies.
It is calculated by using the formula: Volume = (Base Area x Height) / 3 Where the base area is the area of the rectangular base, and the height is the perpendicular distance from the base to the apex of the pyramid.
Volume of Rectangular Pyramid Formula A rectangular pyramid is a 3-dimensional shape with a rectangle as its base.
To calculate its volume, you multiply the area of the base by the height of the pyramid and divide by three.
The formula for the volume of a rectangular pyramid is given as follows: Volume = (Base Area x Height) / 3
How to Derive the Volume of a Rectangular Pyramid?
To derive the volume of a rectangular 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 rectangular pyramid: Base Area = Length x Width The volume of a rectangular pyramid will be, Volume = (Length x Width x Height) / 3
How to find the volume of a rectangular pyramid?
The volume of a rectangular pyramid is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
Calculate the area of the base, multiply it by the height, and then divide by three to find the volume.
Let’s take a look at the formula for finding the volume of a rectangular pyramid: Write down the formula: Volume = (Base Area x Height) / 3 The base area is the area of the rectangular base.
The base area of a rectangular pyramid is the product of its length and width.
This is needed to calculate the volume because it represents the area of the base.
Once we know the base area and the height, substitute those values into the formula Volume = (Base Area x Height) / 3 to find the volume.
Tips and Tricks for Calculating the Volume of Rectangular Pyramid
Remember the formula: The formula for the volume of a rectangular pyramid is: Volume = (Base Area x Height) / 3
Break it down: The volume is how much space fits inside the pyramid. Calculate the base area first, then multiply by the height, and divide by three.
Simplify the numbers: If the base area or height is a simple number, it makes calculations easier.
For example, if the base area is 12 and the height is 6, then the volume is (12 x 6) / 3 = 24.
Check for square roots: If you are given the volume and need to find the height or base dimensions, you may need to rearrange the formula to solve for the missing dimension.
Common Mistakes and How to Avoid Them in Volume of Rectangular Pyramid
Making mistakes while learning the volume of the rectangular pyramid is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of rectangular pyramids.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area.
Surface area involves calculating the areas of all faces, but volume is calculated by using the base area and height.
For example, volume = (Base Area x Height) / 3, not the area of faces.
Mistake 2
Confusing Volume with Lateral Surface Area
Some kids may think of the pyramid’s lateral surface area instead of the volume formula.
Volume is the space inside the pyramid, whereas lateral surface area refers to the total area of the triangular faces. Do not mix them up.
Mistake 3
Using the wrong Formula for different pyramids
Some kids use the formula for the volume of a different type of pyramid instead of the rectangular pyramid formula.
Mistake 4
Confusing cubic volume with linear measurements
Thinking of volume in terms of linear measurements. This happens when someone uses just the height or base dimensions without calculating the base area first.
Mistake 5
Incorrectly calculating the base area
Some students calculate the given volume without properly calculating the base area first.
For example, if the base area is needed, they might forget to multiply the length by the width.
Volume of Rectangular Pyramid Examples
Problem 1
A rectangular pyramid has a base with a length of 5 cm and a width of 3 cm, and its height is 9 cm. What is its volume?
The volume of the rectangular pyramid is 45 cm³.
Explanation
To find the volume of a rectangular pyramid, use the formula: V = (Base Area x Height) / 3 Base Area = 5 cm x 3 cm = 15 cm² V = (15 cm² x 9 cm) / 3 = 45 cm³
Problem 2
A rectangular pyramid has a base area of 20 m² and a height of 12 m. Find its volume.
The volume of the rectangular pyramid is 80 m³.
Explanation
To find the volume of a rectangular pyramid, use the formula: V = (Base Area x Height) / 3 Substitute the base area (20 m²) and height (12 m): V = (20 m² x 12 m) / 3 = 80 m³
Problem 3
The volume of a rectangular pyramid is 150 cm³. Its base has a length of 10 cm and a width of 5 cm. What is the height of the pyramid?
The height of the pyramid is 9 cm.
Explanation
If you know the volume of the pyramid and need to find the height, rearrange the formula: V = (Base Area x Height) / 3
Base Area = 10 cm x 5 cm = 50 cm² 150 cm³ = (50 cm² x Height) / 3 Height = (150 cm³ x 3) / 50 cm² = 9 cm
Problem 4
A rectangular pyramid has a base with a length of 4 inches and a width of 3 inches. Its volume is 24 inches³. Find its height.
The height of the pyramid is 6 inches.
Explanation
Using the formula for volume: V = (Base Area x Height) / 3 Base Area = 4 inches x 3 inches = 12 inches² 24 inches³ = (12 inches² x Height) / 3 Height = (24 inches³ x 3) / 12 inches² = 6 inches
Problem 5
You have a rectangular pyramid with a base length of 6 feet and a width of 4 feet. The height of the pyramid is 10 feet. How much space (in cubic feet) is available inside the pyramid?
The pyramid has a volume of 80 cubic feet.
Explanation
Using the formula for volume: V = (Base Area x Height) / 3 Base Area = 6 feet x 4 feet = 24 feet² V = (24 feet² x 10 feet) / 3 = 80 feet³
FAQs on Volume of Rectangular Pyramid
1.Is the volume of a rectangular 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 dimensions be a decimal or fraction?
5.Is the volume of a rectangular pyramid the same as the lateral surface area?
Important Glossaries for Volume of Rectangular Pyramid
- Base Area: The area of the rectangular base of the pyramid. It is calculated by multiplying the length and width of the base.
- Height: The perpendicular distance from the base to the apex of the pyramid.
- Volume: The amount of space enclosed within a 3D object. In the case of a rectangular pyramid, the volume is calculated by multiplying the base area by the height and dividing by three. It is expressed in cubic units (e.g., cm³, m³).
- Rectangular Pyramid: A 3-dimensional shape with a rectangular base and four triangular faces that meet at an apex.
- Cubic Units: The units of measurement used for volume. If the base dimensions are in centimeters (cm), the volume will be in cubic centimeters (cm³); if in meters, cubic meters (m³).
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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
