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Last updated on July 9th, 2025

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Volume of Right Pyramid

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The volume of a right pyramid is the total space it occupies or the number of cubic units it can hold. A right pyramid is a 3D shape with a polygonal base and triangular faces that meet at a common vertex. To find the volume of a right pyramid, we use the formula involving its base area and height. In real life, kids can relate to the volume of a right pyramid by thinking of objects like tents or the Great Pyramid of Giza. In this topic, let’s learn about the volume of the right pyramid.

Volume of Right Pyramid for US Students
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What is the volume of a right pyramid?

The volume of a right pyramid is the amount of space it occupies. It is calculated by using the formula: Volume = (1/3) × Base Area × Height

 

Where 'Base Area' is the area of the polygonal base, and 'Height' is the perpendicular distance from the base to the apex.

 

Volume of Right Pyramid Formula A right pyramid is a 3-dimensional shape with a polygonal base and triangular faces converging at a point (the apex). To calculate its volume, you multiply the base area by the height and then divide by three.

 

The formula for the volume of a right pyramid is given as follows: Volume = (1/3) × Base Area × Height

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How to Derive the Volume of a Right Pyramid?

To derive the volume of a right pyramid, we use the concept of volume as the total space occupied by a 3D object. The volume formula for pyramids is derived from the relationship between the base area, height, and the apex.

 

The formula for the volume of any pyramid is: Volume = (1/3) × Base Area × Height For a right pyramid, the height is the perpendicular distance from the base to the apex.

 

The volume of a right pyramid will be, Volume = (1/3) × Base Area × Height

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How to find the volume of a right pyramid?

The volume of a right pyramid is always expressed in cubic units, for example, cubic centimeters 'cm³', cubic meters 'm³'. First, calculate the base area, and multiply it by the height, then divide by three, to find the volume.

 

Let’s take a look at the formula for finding the volume of a right pyramid: Write down the formula Volume = (1/3) × Base Area × Height Base

 

Area is the area of the base polygon. Height is the perpendicular distance from the base to the apex. Once you know the base area and the height, substitute those values into the formula.

 

To find the volume, multiply the base area by the height, and divide by three.

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Tips and Tricks for Calculating the Volume of Right Pyramid

  • Remember the formula: The formula for the volume of a right pyramid is simple: Volume = (1/3) × Base Area × Height

 

  • Break it down: The volume is how much space fits inside the pyramid. Calculate the base area first, then multiply it by the height, and finally divide by three.

 

  • Simplify the numbers: If the base area and height are simple numbers, it is easy to calculate.

 

  • Check for correct base area Ensure you accurately calculate the base area, especially for non-standard polygons.
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Common Mistakes and How to Avoid Them in Volume of Right Pyramid

Making mistakes while learning the volume of the right pyramid is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of right pyramids.

Mistake 1

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Confusing Volume with Surface Area

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Some students confuse the formula for volume with the formula for surface area. Surface area is calculated by adding the area of all faces, but volume is calculated using the base area and height.

 

For example, the volume is (1/3) × Base Area × Height, not the sum of all face areas.

Mistake 2

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Confusing Volume with Base Area

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Some kids may think of the base area instead of the volume formula. Volume is the space inside the pyramid, whereas base area refers to the area of the polygonal base. Do not mix them up.

Mistake 3

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Using the wrong Formula for Prisms

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Some kids use the formula for the volume of a prism (Base Area × Height) instead of the pyramid formula, which requires dividing by three.

Mistake 4

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Confusing height with slant height

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Using the slant height (the diagonal distance along the face) instead of the perpendicular height. Ensure you use the perpendicular height in the volume formula.

Mistake 5

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Incorrectly calculating the base area

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Some students calculate the given base area incorrectly. Make sure to correctly calculate the area of the base polygon before using it in the volume formula.

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Volume of Right Pyramid Examples

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Problem 1

A right pyramid has a square base with a side length of 4 cm and a height of 6 cm. What is its volume?

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The volume of the right pyramid is 32 cm³.

Explanation

To find the volume of a right pyramid, use the formula: V = (1/3) × Base Area × Height

 

Here, the base is a square with side length 4 cm, so the base area is 4 × 4 = 16 cm².

 

Height is 6 cm, so: V = (1/3) × 16 × 6 = 32 cm³

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Problem 2

A right pyramid has a triangular base with a base length of 5 m, a height of 4 m, and a pyramid height of 9 m. Find its volume.

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The volume of the right pyramid is 30 m³.

Explanation

To find the volume of a right pyramid, use the formula: V = (1/3) × Base Area × Height

 

The base is a triangle with base length 5 m and height 4 m, so the base area is (1/2) × 5 × 4 = 10 m².

 

Pyramid height is 9 m, so: V = (1/3) × 10 × 9 = 30 m³

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Problem 3

The volume of a right pyramid is 48 cm³. The base area is 24 cm². What is the height of the pyramid?

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The height of the pyramid is 6 cm.

Explanation

If you know the volume of the pyramid and the base area, you can find the height using the formula: Volume = (1/3) × Base Area × Height 48 = (1/3) × 24 × Height

 

Height = 48 × 3 / 24 = 6 cm

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Problem 4

A right pyramid has a rectangular base measuring 3 inches by 5 inches and a height of 10 inches. Find its volume.

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The volume of the right pyramid is 50 inches³.

Explanation

Using the formula for volume: V = (1/3) × Base Area × Height

 

The base is a rectangle with area 3 × 5 = 15 inches². Height is 10 inches,

 

so: V = (1/3) × 15 × 10 = 50 inches³

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Problem 5

You have a right pyramid with a hexagonal base with an area of 54 ft² and a height of 12 ft. How much space (in cubic feet) is available inside the pyramid?

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The pyramid has a volume of 216 ft³.

Explanation

Using the formula for volume: V = (1/3) × Base Area × Height

 

Base area is 54 ft² and height is 12 ft, so: V = (1/3) × 54 × 12 = 216 ft³

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FAQs on Volume of Right Pyramid

1.Is the volume of a right pyramid the same as the surface area?

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2.How do you find the volume if the base area and height are given?

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3.What if I have the volume and base area and need to find the height?

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4.Can the base be any polygonal shape?

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5.Is the volume of a right pyramid the same as the surface area?

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Important Glossaries for Volume of Right Pyramid

  • Base Area: The area of the polygonal base of the pyramid.

 

  • Height: The perpendicular distance from the base to the apex of the pyramid.

 

  • Volume: The amount of space enclosed within the pyramid, calculated using the base area and height.

 

  • Perpendicular Height: The distance from the base to the apex, measured at a right angle to the base.

 

  • Cubic Units: The units of measurement used for volume, such as cubic centimeters (cm³) or 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.

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Fun Fact

: She has songs for each table which helps her to remember the tables

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