Volume of Elongated Square Pyramid Given Height Calculator

Volume of Elongated Square Pyramid Formula:

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

Volume of Elongated Square Pyramid:

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1. What is the 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 formed by attaching a square pyramid to a cube.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Elongated Square Pyramid (m³)
\( h \) — Height of Elongated Square Pyramid (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the volume based on the height of the elongated square pyramid, incorporating the geometric relationships between its components.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific applications where spatial measurements are required.

4. Using the Calculator

Tips: Enter the height of the elongated square pyramid in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is an elongated square pyramid?
A: An elongated square pyramid is a polyhedron formed by attaching a square pyramid to a cube, creating a geometric solid with a square base and triangular sides meeting at an apex.

Q2: Why is the square root of 2 used in the formula?
A: The square root of 2 appears naturally in geometric calculations involving squares and right triangles, particularly in relationships between side lengths and diagonals.

Q3: What are typical applications of this calculation?
A: This calculation is used in architecture, 3D modeling, packaging design, and any field requiring precise volume measurements of complex geometric shapes.

Q4: Can this formula be used for any elongated pyramid?
A: No, this specific formula applies only to elongated square pyramids. Other pyramid types with different base shapes would require different formulas.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric shapes. Real-world applications may require adjustments for material thickness and manufacturing tolerances.