1. What is a Truncated Rectangular Pyramid?

A truncated rectangular pyramid (also called a rectangular frustum) is a pyramid with the top cut off by a plane parallel to the base. It has two rectangular bases of different sizes and trapezoidal sides.

2. How Does the Calculator Work?

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

Where:

• \( h \) — Height between the two bases
• \( l_1 \) — Length of the first (bottom) base
• \( w_1 \) — Width of the first (bottom) base
• \( l_2 \) — Length of the second (top) base
• \( w_2 \) — Width of the second (top) base

Explanation: The formula accounts for both the top and bottom rectangular areas plus their geometric mean.

3. Applications of This Calculation

Details: This calculation is used in architecture, construction, 3D modeling, and any field requiring volume calculations for pyramidal structures with truncated tops.

4. Using the Calculator

Tips: Enter all dimensions in the same units. The height must be perpendicular to both bases. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if the top isn't parallel to the base?
A: This formula only works when the truncation plane is parallel to the base. For non-parallel truncations, more complex calculations are needed.

Q2: Can I use different units for different dimensions?
A: No, all dimensions must be in the same units for the calculation to be valid.

Q3: What's the difference between this and a regular pyramid volume?
A: A regular pyramid has a point at the top (l₂ = w₂ = 0), while a truncated pyramid has a rectangular top.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric shapes. Real-world objects may have imperfections.

Q5: Can this be used for trapezoidal prisms?
A: No, this formula is specific to truncated rectangular pyramids. Trapezoidal prisms have different volume formulas.