Volume of Gyroelongated Square Pyramid Given Height Calculator

Formula Used:

\[ V = \frac{\sqrt{4 + 3\sqrt{2}} + \frac{1}{\sqrt{2}}}{3} \times \left( \frac{h}{\sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \frac{1}{\sqrt{2}}} \right)^3 \]

Volume of Gyroelongated Square Pyramid:

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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:

\[ V = \frac{\sqrt{4 + 3\sqrt{2}} + \frac{1}{\sqrt{2}}}{3} \times \left( \frac{h}{\sqrt{1 - \frac{1}{2 + \sqrt{2}}} + \frac{1}{\sqrt{2}}} \right)^3 \]

Where:

\( V \) — Volume of Gyroelongated Square Pyramid (m³)
\( h \) — Height of Gyroelongated Square Pyramid (m)

Explanation: This formula calculates the volume based on the height of the gyroelongated square pyramid, incorporating square root functions and mathematical constants.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, and mathematics education. It helps in material estimation, structural analysis, and understanding spatial relationships.

4. Using the Calculator

Tips: Enter the height of the gyroelongated square pyramid in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a gyroelongated square pyramid?
A: A gyroelongated square pyramid is a Johnson solid created by attaching a square pyramid to a square antiprism, resulting in a polyhedron with triangular and square faces.

Q2: What units should I use for the height?
A: The calculator uses meters as the unit for height, but you can convert from other units as long as you maintain consistency.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise based on the given formula, though practical measurements may have some margin of error.

Q4: Can this formula be used for other pyramid types?
A: No, this specific formula is designed only for gyroelongated square pyramids. Other pyramid types have different volume formulas.

Q5: What are the practical applications of this calculation?
A: This calculation is useful in architectural design, 3D modeling, educational contexts, and any application requiring precise volume measurements of this specific geometric shape.