Priority 2 • Leaning / Tilted Pyramids

Oblique Pyramid Volume Calculator

An oblique pyramid has an apex that is not centered directly above the centroid of the base. By Cavalieri’s principle, its volume depends strictly on base area and true vertical height.

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Step-by-Step Mathematical Solution

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Primary Mathematical Formula

$$V = \frac{1}{3} A_b h$$

Frequently Asked Questions

How do you calculate the volume of an oblique pyramid?

Multiply the base area by the perpendicular height and divide by 3. The apex does not have to sit directly above the centre of the base.

What is the formula for an oblique pyramid?

The formula is $V = \frac{1}{3} B h$, where $B$ is the base area and $h$ is the perpendicular altitude from the apex dropped at a 90° angle to the plane containing the base.

Is an oblique pyramid different from a right pyramid?

Yes. In a right pyramid, the apex is positioned perpendicularly above the geometric centroid of the base. In an oblique pyramid, the apex is shifted or tilted to one side.

Does the tilted shape affect an oblique pyramid's volume?

By Cavalieri's Principle, the tilt itself does not change the volume. Enclosed volume depends strictly on base area and perpendicular vertical height.

Can I use the slant height of an oblique pyramid?

Not directly. In an oblique pyramid, every sloping face has a different slant height. The volume formula requires the perpendicular vertical altitude $h$.