Volume of Anticube given Total Surface Area Calculator

Formula Used:

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

Volume of Anticube:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Volume of Anticube?

The volume of an anticube is the amount of 3-dimensional space enclosed by the surface of the anticube. It represents the capacity or the space occupied by this unique geometric shape.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Anticube (m³)
\( TSA \) — Total Surface Area of Anticube (m²)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the volume of an anticube based on its total surface area, using mathematical constants and square root operations.

3. Importance of Volume Calculation

Details: Calculating the volume of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in understanding spatial relationships and material requirements.

4. Using the Calculator

Tips: Enter the total surface area of the anticube in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an anticube?
A: An anticube is a geometric shape that represents the dual polyhedron of a cube, with specific mathematical properties and characteristics.

Q2: Why is the formula so complex?
A: The complexity arises from the mathematical relationships between surface area and volume in this particular geometric shape, involving square roots and constants.

Q3: What units should I use?
A: Use consistent units (typically meters for length and square meters for area) to ensure accurate volume calculation in cubic meters.

Q4: Can this calculator handle very large or small values?
A: Yes, the calculator can handle a wide range of values, but extremely large or small numbers may be limited by PHP's floating-point precision.

Q5: Is this formula applicable to all anticubes?
A: Yes, this formula is universally applicable to all anticubes as it's derived from the fundamental geometric properties of the shape.