1. What is the Volume of Gyroelongated Square Pyramid?

The volume of a gyroelongated square pyramid represents the total three-dimensional space enclosed by its surface. It is a Johnson solid formed by attaching a square pyramid to a square antiprism.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( V \) — Volume of Gyroelongated Square Pyramid
• \( l_e \) — Edge Length of the pyramid

Explanation: This formula combines geometric properties of both the square pyramid and square antiprism components to calculate the total volume.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is fundamental in mathematics, engineering, and architecture for determining capacity, material requirements, and structural properties.

4. Using the Calculator

Tips: Enter the edge length in meters. The value must be positive and valid. The calculator will compute the volume using the precise mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is a gyroelongated square pyramid?
A: A gyroelongated square pyramid is a Johnson solid (J10) created by attaching a square pyramid to a square antiprism.

Q2: What are the units for volume calculation?
A: The volume is calculated in cubic meters (m³) when edge length is provided in meters.

Q3: Can this calculator handle different units?
A: The calculator uses the input unit consistently. If you enter edge length in centimeters, the volume will be in cubic centimeters.

Q4: How accurate is the calculation?
A: The calculation uses precise mathematical constants and provides results with 6 decimal places accuracy.

Q5: What applications does this calculation have?
A: This calculation is useful in geometry education, architectural design, and engineering applications involving complex polyhedra.