Surface to Volume Ratio of Antiprism Given Volume Calculator

Surface to Volume Ratio Formula:

\[ \text{RA/V} = \frac{6(\sin(\pi/N))^2(\cot(\pi/N)+\sqrt{3})}{\sin(\frac{3\pi}{2N})\sqrt{4\cos^2(\pi/2N)-1} \cdot \left(\frac{12(\sin(\pi/N))^2 V}{N\sin(\frac{3\pi}{2N})\sqrt{4\cos^2(\pi/2N)-1}}\right)^{1/3}} \]

Surface to Volume Ratio (RA/V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface to Volume Ratio of Antiprism?

The Surface to Volume Ratio of an Antiprism is a geometric property that describes the relationship between the total surface area and the volume of the antiprism. It's an important parameter in various engineering and mathematical applications.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

\( N \) — Number of vertices
\( V \) — Volume of the antiprism (m³)
\( \pi \) — Mathematical constant pi (≈3.14159)

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is crucial in materials science, heat transfer, and chemical reactions where surface area affects reaction rates and efficiency.

4. Using the Calculator

Tips: Enter the number of vertices (must be ≥3) and the volume (must be positive). The calculator will compute the surface to volume ratio using trigonometric functions.

5. Frequently Asked Questions (FAQ)

Q1: What is an antiprism?
A: An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles.

Q2: Why is surface to volume ratio important?
A: It indicates how much surface area is available per unit volume, which affects properties like heat dissipation, chemical reactivity, and structural strength.

Q3: What are typical values for this ratio?
A: The ratio depends on the number of vertices and volume. Smaller volumes and more vertices generally yield higher surface to volume ratios.

Q4: Can this calculator handle decimal inputs?
A: Number of vertices must be an integer ≥3, while volume can be any positive decimal number.

Q5: What units are used?
A: Volume is in cubic meters (m³) and the resulting ratio is in inverse meters (m⁻¹).