Last updated on July 9th, 2025
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.
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
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
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.
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.
A right pyramid has a square base with a side length of 4 cm and a height of 6 cm. What is its volume?
The volume of the right pyramid is 32 cm³.
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
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.
The volume of the right pyramid is 30 m³.
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
The volume of a right pyramid is 48 cm³. The base area is 24 cm². What is the height of the pyramid?
The height of the pyramid is 6 cm.
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
A right pyramid has a rectangular base measuring 3 inches by 5 inches and a height of 10 inches. Find its volume.
The volume of the right pyramid is 50 inches³.
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
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?
The pyramid has a volume of 216 ft³.
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
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.
: She has songs for each table which helps her to remember the tables