Volume of a Pyramid Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the volume of a pyramid?
Answer
Volume of a pyramid
V = (1/3) · a · b · h
Here a is the side (or base), b is the second side, h is the height, perpendicular to the base. The result comes out in cubic units.
Where the formula comes from
V = (1/3) · a · b · h
The same one third as the cone, and for the same reason: three pyramids of equal base and equal height fill the prism built on that base. Swap the rectangular base for a circle and this formula becomes the cone’s.
Worked examples
Let a = 6, b = 6, h = 9. Then the volume of a pyramid = 108 cubic units.
Let a = 4, b = 5.5, h = 3. Then the volume of a pyramid = 22 cubic units.
The common mistake
Using the edge of a face as the height. The height runs from the apex straight down to the base plane; the sloping edge and the slant height of a face are both longer, and all three are different numbers.
Other quantities: Pyramid
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the volume of a pyramid? (The answer is: V = (1/3) · a · b · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Values from the Formula (b = 6, h = 9)
| If a = | Volume |
|---|---|
| 1 | 18 cubic units |
| 2 | 36 cubic units |
| 3 | 54 cubic units |
| 4 | 72 cubic units |
| 5 | 90 cubic units |
| 10 | 180 cubic units |
FAQ
What is the formula for the volume of a pyramid?
Volume of a pyramid V = (1/3) · a · b · h
Where does this formula come from?
The same one third as the cone, and for the same reason: three pyramids of equal base and equal height fill the prism built on that base. Swap the rectangular base for a circle and this formula becomes the cone’s.
What is the most common mistake here?
Using the edge of a face as the height. The height runs from the apex straight down to the base plane; the sloping edge and the slant height of a face are both longer, and all three are different numbers.
How do I use this formula?
Put your own numbers in place of the letters. With a = 4, b = 5.5, h = 3, for instance, the formula V = (1/3) · a · b · h gives = 22 cubic units.
See Also
- Surface Area of a Cone Formula
- Surface Area of a Cube Formula
- Surface Area of a Cylinder Formula
- Surface Area of a Pyramid Formula
- Surface Area of a Rectangular Prism Formula
- Surface Area of a Sphere Formula
- Surface Area of a Triangular Prism Formula
- Volume of a Cone Formula
- Volume of a Cube Formula
- Volume of a Cylinder Formula
- Volume of a Rectangular Prism Formula
- Volume of a Sphere Formula
- Volume of a Triangular Prism Formula
- Объём пирамиды
- Volumen de la pirámide
- Volume da pirâmide