1. What is a Truncated Pyramid?

A truncated pyramid (or frustum of a pyramid) is the portion of a pyramid between two parallel planes cutting it. It has two bases - a larger bottom base and a smaller top base - and trapezoidal lateral faces.

2. How Does the Calculator Work?

The calculator uses the volume formula for a truncated pyramid:

Where:

• \( h \) — Height between the two bases
• \( A1 \) — Area of the bottom base
• \( A2 \) — Area of the top base

Explanation: The formula accounts for the contribution of both base areas and their geometric mean to determine the volume.

3. Applications of Truncated Pyramid Volume

Details: This calculation is used in architecture, engineering, and geometry problems involving storage tanks, building structures, and geological formations.

4. Using the Calculator

Tips: Enter height and both base areas in consistent units. All values must be positive numbers. The calculator will output volume in cubic units.

5. Frequently Asked Questions (FAQ)

Q1: What if the bases are different shapes?
A: The formula works as long as you know the areas of both bases. The shapes can be any polygon (square, rectangle, etc.).

Q2: How accurate is this formula?
A: It's mathematically exact for perfect truncated pyramids with parallel bases.

Q3: Can this be used for cones?
A: Yes, for truncated cones (frustums), use the same formula with circular base areas (πr²).

Q4: What units should I use?
A: Use consistent units (e.g., all in meters for height and square meters for areas).

Q5: How does this relate to full pyramid volume?
A: If A2 = 0, it reduces to the standard pyramid volume formula (V = (1/3) × A1 × h).