Surface Area of Oloid given Surface to Volume Ratio Calculator

Surface Area of Oloid Formula:

\[ SA = (4\pi) \times \left(\frac{4\pi}{3.0524184684 \times \frac{RA}{V}}\right)^2 \]

Surface Area of Oloid:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Surface Area of Oloid?

The Surface Area of Oloid is the total area that the surface of the oloid occupies. An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA = (4\pi) \times \left(\frac{4\pi}{3.0524184684 \times \frac{RA}{V}}\right)^2 \]

Where:

\( SA \) — Surface Area of Oloid (m²)
\( \frac{RA}{V} \) — Surface to Volume Ratio of Oloid (1/m)
\( \pi \) — Archimedes' constant (approximately 3.14159)
3.0524184684 — Constant specific to oloid geometry

Explanation: This formula calculates the surface area of an oloid based on its surface to volume ratio, using mathematical constants specific to oloid geometry.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of an oloid is important in various engineering and design applications, particularly in fluid dynamics, architectural design, and mathematical modeling where this unique geometric shape is utilized.

4. Using the Calculator

Tips: Enter the surface to volume ratio of the oloid in 1/m. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an oloid?
A: An oloid is a three-dimensional curved geometric shape discovered by Paul Schatz. It's the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes.

Q2: What are typical applications of oloids?
A: Oloids are used in various applications including mixing devices, architectural designs, and as mathematical objects of study due to their unique rolling properties and constant width.

Q3: Why is the constant 3.0524184684 used?
A: This constant is derived from the mathematical properties of the oloid shape and is specific to the relationship between surface area and volume in oloid geometry.

Q4: What units should be used for input?
A: The surface to volume ratio should be entered in reciprocal meters (1/m), and the result will be in square meters (m²).

Q5: Can this calculator be used for other geometric shapes?
A: No, this calculator is specifically designed for oloid geometry. Other shapes have different mathematical relationships between surface area and volume.