Volume of Elongated Square Pyramid given Total Surface Area Calculator

Formula Used:

\[ V = \left(1 + \frac{\sqrt{2}}{6}\right) \times \left(\sqrt{\frac{TSA}{5 + \sqrt{3}}}\right)^3 \]

Volume of Elongated Square Pyramid (V):

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1. What is Volume of Elongated Square Pyramid?

The Volume of Elongated Square Pyramid represents the total three-dimensional space enclosed by the surface of an Elongated Square Pyramid, which is a geometric solid formed by attaching a square pyramid to a cube.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \left(1 + \frac{\sqrt{2}}{6}\right) \times \left(\sqrt{\frac{TSA}{5 + \sqrt{3}}}\right)^3 \]

Where:

\( V \) — Volume of Elongated Square Pyramid (m³)
\( TSA \) — Total Surface Area (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula derives the volume from the total surface area by solving for the edge length and then calculating the volume.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric solids is essential in various fields including architecture, engineering, manufacturing, and 3D modeling for determining capacity, material requirements, and spatial relationships.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid. The calculator will compute the corresponding volume.

5. Frequently Asked Questions (FAQ)

Q1: What is an Elongated Square Pyramid?
A: An Elongated Square Pyramid is a Johnson solid formed by attaching a square pyramid to one face of a cube, creating a polyhedron with 9 faces (4 triangles and 5 squares).

Q2: Why is the formula structured this way?
A: The formula reverses the surface area calculation to find the edge length, then uses the standard volume formula for this specific geometric shape.

Q3: What are the units for the result?
A: The volume is calculated in cubic meters (m³) when surface area is provided in square meters (m²).

Q4: Can this calculator handle different units?
A: The calculator uses consistent units. If you input surface area in different units, the volume will be in the corresponding cubic units.

Q5: What is the practical application of this calculation?
A: This calculation is useful in architectural design, packaging optimization, and any application involving the geometric properties of elongated square pyramid shapes.