Volume of a Square Pyramid
The volume of a square pyramid measures the amount of three-dimensional space enclosed by the pyramid. It is calculated using the formula V = (1/3)s²h, where s is the length of the base side and h is the perpendicular height from the base to the apex.
The Volume Formula Explained
Standard Formula
Volume equals one-third of the base area times height.
V = (1/3) x s² x h
Why 1/3?
A pyramid occupies exactly one-third the volume of a prism with the same base and height.
V_pyramid = (1/3) x V_prism
Using Base Area
If you already know the base area B, use V = (1/3)Bh.
V = (1/3) x B x h
How to Calculate Step by Step
- Measure the side length (s) of the square base.
- Measure the perpendicular height (h) from base to apex.
- Calculate the base area: A = s².
- Multiply: V = (1/3) x A x h.
Example Calculation
For a square pyramid with base side 6 units and height 9 units: V = (1/3)(6²)(9) = (1/3)(36)(9) = (1/3)(324) = 108 cubic units.
Common Mistakes to Avoid
- Confusing slant height with perpendicular height - always use the perpendicular height h.
- Forgetting to divide by 3 - a pyramid is 1/3 of a prism, not the full prism.
- Using diameter instead of side length for the base measurement.