1. What is a Truncated Square Pyramid?

A truncated square pyramid (also called a frustum of a square pyramid) is a three-dimensional shape formed by cutting the top off a square pyramid with a plane parallel to the base. It has two square bases (one larger, one smaller) and four trapezoidal faces.

2. How Does the Calculator Work?

The calculator uses the volume formula for a truncated square pyramid:

Where:

• \( h \) — Height (distance between bases)
• \( a \) — Side length of the first square base
• \( b \) — Side length of the second square base

Explanation: The formula accounts for the contributions of both square bases and their interaction in determining the volume.

3. Importance of Volume Calculation

Details: Calculating the volume of a truncated pyramid is essential in architecture, engineering, and geometry applications where this shape appears in structures or design elements.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if the bases aren't parallel?
A: This formula only works for a true truncated pyramid where the smaller base is parallel to the larger base.

Q2: Can this be used for rectangular bases?
A: No, this formula is specifically for square bases. For rectangular bases, a different formula is needed.

Q3: What are common real-world examples?
A: Buckets, certain architectural elements, and some types of lampshades often have this shape.

Q4: How precise should my measurements be?
A: For practical applications, measure to the precision needed for your project. The calculator accepts up to 4 decimal places.

Q5: What if the height is measured at an angle?
A: The height must be the perpendicular distance between the two bases for the formula to be accurate.