Calculate volume of a truncated pyramid
Formula:
V = (1/3) * h * (A₁ + A₂ + √(A₁ * A₂))
Where A₁ and A₂ are the areas of the top and bottom bases, and h is the height.
Measure the top base dimensions and calculate its area (A₁).
Why: The top area is one of the three components in the volume formula. It's usually smaller than the base.
Measure the bottom base dimensions and calculate its area (A₂).
Why: The bottom base is typically larger. For similar pyramids, ratio A₂/A₁ relates to (R₃) where R is the scaling factor.
Measure the perpendicular distance between the two parallel base planes.
Why: Height must be perpendicular to both bases. Slant measurements give incorrect results.
Compute √(A₁ * A₂) as part of the formula.
Why: The geometric mean of the two base areas appears in the formula. It represents the average cross-sectional area through the frustum.
Check that all values are positive and the volume makes geometric sense.
Why: Volume should be between that of a prism with area A₁ and one with area A₂. Extreme values indicate errors.
Truncated Pyramid Storage Tank
Related Tools