1. What is the Truncated Pyramid Volume Formula?

The truncated pyramid (or frustum) volume formula calculates the space occupied by a pyramid with the top cut off parallel to the base. It's commonly used in geometry, architecture, and engineering.

2. How Does the Calculator Work?

The calculator uses the truncated pyramid volume formula:

Where:

• \( V \) — Volume of the truncated pyramid
• \( h \) — Height between the two parallel bases
• \( A_1 \) — Area of the lower base
• \( A_2 \) — Area of the upper base

Explanation: The formula accounts for both base areas and their geometric mean, scaled by one-third of the height.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for material estimation in construction, storage capacity planning, and geometric analysis in various engineering fields.

4. Using the Calculator

Tips: Enter height in units, both base areas in square units. All values must be positive numbers. The calculator automatically computes the 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 parallel bases, regardless of their shape (square, rectangle, circle, etc.).

Q2: How does this relate to a full pyramid?
A: If A₂ = 0, the formula reduces to the standard pyramid volume formula V = (h × A₁)/3.

Q3: What units should I use?
A: Use consistent units - height in linear units and areas in square units of the same measurement system.

Q4: Can this be used for cones?
A: Yes, for truncated cones (frustums), just use the circular area formula πr² for A₁ and A₂.

Q5: What's the geometric interpretation?
A: The formula averages the three areas: the two base areas and their geometric mean (√(A₁A₂)).