Frustum Volume
Calculator
Results
- Volume
- 224
- Bottom face area
- 64
- Top face area
- 16
Results
| Volume | 224 |
| Bottom face area | 64 |
| Top face area | 16 |
formula-map diagram
- Volume
- 224
- Bottom face area
- 64
- Top face area
- 16
Formula map
Formula
V = (h/3) × (A₁ + A₂ + √(A₁ × A₂))= 224
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
More in Advanced geometry
See all →Frequently asked questions
What is a frustum, and how is its volume different from a full pyramid's?+
A frustum is what remains when the top of a pyramid or cone is sliced off by a plane parallel to the base, leaving two parallel faces of different sizes. Its volume is calculated as the volume of the full pyramid minus the volume of the smaller pyramid that was removed from the top.
What is the frustum volume formula, and what do the terms mean?+
For a pyramidal frustum, V = (h/3)(A₁ + A₂ + √(A₁A₂)), where h is the perpendicular height between the two parallel faces, and A₁ and A₂ are the areas of the bottom and top faces. The √(A₁A₂) cross term accounts for the tapering shape between the two different-sized faces.
Why isn't the frustum volume simply the average of the two face areas times height?+
Because the sides taper in a specific geometric way (following the original pyramid's proportions), a simple average would overestimate the actual enclosed volume. The geometric mean term √(A₁A₂) correctly accounts for this taper, which is why it appears instead of a simple arithmetic average.
What happens to the formula if the top face area shrinks to zero?+
If A₂ = 0, the formula correctly reduces to V = (h/3)A₁, which is exactly the standard pyramid volume formula. This confirms the frustum formula is consistent with a full pyramid as a limiting case where the cut is made at the very apex.
Does this formula work for a cone-shaped frustum, like a lampshade or a bucket, too?+
Yes, the same formula applies whether the parallel cross-sections are circles (a conical frustum) or polygons (a pyramidal frustum), since both A₁ and A₂ are simply plugged in as areas. This is why the frustum formula is the standard approach for practical shapes like buckets, lampshades, and truncated silos.