Volume of a Pyramid
Calculate the volume of a pyramid using V = (1/3)Bh.
Works for any pyramid shape — square, rectangular, or triangular base.
The Formula
V = (1/3) × B × h
The volume of a pyramid is one-third of the base area multiplied by the height.
This works for any pyramid, regardless of the shape of its base.
Variables
| Symbol | Meaning |
|---|---|
| V | Volume of the pyramid |
| B | Area of the base (calculate using the appropriate area formula) |
| h | Height of the pyramid (measured perpendicular to the base) |
Example 1
Find the volume of a pyramid with a square base of 6 m sides and height 10 m
Base area B = 6 × 6 = 36 m²
V = (1/3) × B × h = (1/3) × 36 × 10
V = (1/3) × 360
V = 120 m³
Example 2
A pyramid has a rectangular base of 8 cm by 5 cm and a height of 12 cm
Base area B = 8 × 5 = 40 cm²
V = (1/3) × 40 × 12 = (1/3) × 480
V = 160 cm³
When to Use It
Use the volume of a pyramid formula when:
- Calculating the volume of pyramid-shaped structures or objects
- Working with architectural or historical pyramid measurements
- Solving 3D geometry problems involving pyramids
- Comparing volumes — a pyramid is always 1/3 the volume of a prism with the same base and height