Surface to Volume Ratio of Gyroelongated Square Pyramid given Height Calculator

Formula Used:

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

Surface to Volume Ratio (SA:V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Gyroelongated Square Pyramid?

The Surface to Volume Ratio (SA:V) of a Gyroelongated Square Pyramid is the numerical ratio of its total surface area to its volume. It provides insight into the efficiency of surface area relative to volume for this specific geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( h \) — Height of the Gyroelongated Square Pyramid (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)
\( \sqrt{3} \) — Square root of 3 (approximately 1.7321)

Explanation: This formula calculates the surface to volume ratio based on the height of the gyroelongated square pyramid, incorporating geometric relationships specific to this polyhedron.

3. Importance of Surface to Volume Ratio Calculation

Details: The surface to volume ratio is important in various fields including materials science, chemistry, and engineering. It helps understand properties like heat transfer, reaction rates, and structural efficiency for this particular geometric shape.

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 constructed by attaching a square antiprism to the square base of a square pyramid.

Q2: What units are used for the surface to volume ratio?
A: The surface to volume ratio is measured in reciprocal meters (m⁻¹), as it represents area per unit volume.

Q3: How does height affect the surface to volume ratio?
A: The surface to volume ratio typically decreases as the size of the object increases, following inverse proportionality.

Q4: What are typical values for this ratio?
A: Values vary depending on the height, but generally fall within a specific range characteristic of this geometric shape.

Q5: Can this calculator be used for other polyhedra?
A: No, this calculator is specifically designed for gyroelongated square pyramids. Other polyhedra have different formulas for surface to volume ratio.