Total Surface Area Of Elongated Square Pyramid Given Surface To Volume Ratio Calculator

Formula Used:

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

Total Surface Area of Elongated Square Pyramid:

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1. What is Total Surface Area of Elongated Square Pyramid?

The Total Surface Area of an Elongated Square Pyramid refers to the complete area covering all its faces, including the square base and the four triangular faces. It is a key geometric measurement in three-dimensional space.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( TSA \) — Total Surface Area of Elongated Square Pyramid (m²)
\( AV \) — SA:V of Elongated Square Pyramid (1/m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)
\( \sqrt{2} \) — Square root of 2 (approximately 1.414)

Explanation: This formula calculates the total surface area based on the surface area to volume ratio of the elongated square pyramid.

3. Importance of Surface Area Calculation

Details: Calculating the total surface area is essential for various applications including material estimation, structural analysis, and geometric modeling in engineering and architecture.

4. Using the Calculator

Tips: Enter the SA:V (Surface Area to Volume Ratio) value in 1/m. The value must be greater than 0 for accurate calculation.

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 square prism, creating a unique geometric shape.

Q2: Why is surface area important in geometry?
A: Surface area calculations are crucial for determining material requirements, heat transfer properties, and structural integrity in various applications.

Q3: How accurate is this calculation?
A: The calculation provides precise results based on the mathematical formula, with accuracy dependent on the input value provided.

Q4: Can this calculator be used for other pyramid shapes?
A: No, this specific calculator is designed only for elongated square pyramids with the given formula.

Q5: What units should I use for the input?
A: The SA:V ratio should be entered in reciprocal meters (1/m) for proper calculation.