Home Back

Total Surface Area of Cuboctahedron given Lateral Surface Area Calculator

Formula Used:

\[ TSA = \frac{2 \times (3 + \sqrt{3}) \times LSA}{(2 \times \sqrt{3}) + 4} \]

Unit Converter ▲

Unit Converter ▼

From: To:

1. What is Total Surface Area of Cuboctahedron?

The Total Surface Area of a Cuboctahedron is defined as the measure of the total amount of two-dimensional space enclosed by all the faces of the Cuboctahedron. It represents the sum of the areas of all 14 faces (8 triangular and 6 square faces) of this Archimedean solid.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ TSA = \frac{2 \times (3 + \sqrt{3}) \times LSA}{(2 \times \sqrt{3}) + 4} \]

Where:

Explanation: This formula establishes the relationship between the lateral surface area and the total surface area of a cuboctahedron, taking into account the geometric properties of this polyhedron.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area is crucial for various applications including material science, architecture, engineering design, and geometric analysis. It helps determine the amount of material needed to construct a cuboctahedron or to calculate its surface properties.

4. Using the Calculator

Tips: Enter the lateral surface area of the cuboctahedron in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding total surface area.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cuboctahedron?
A: A cuboctahedron is an Archimedean solid with 8 triangular faces and 6 square faces, 12 identical vertices, and 24 identical edges.

Q2: What's the difference between lateral surface area and total surface area?
A: Lateral surface area typically excludes the top and bottom faces, while total surface area includes all faces of the polyhedron.

Q3: Can this formula be used for any size of cuboctahedron?
A: Yes, the formula is scalable and works for cuboctahedrons of any size as long as the proportions remain consistent.

Q4: What are practical applications of cuboctahedrons?
A: Cuboctahedrons are used in molecular structures, architectural designs, and various engineering applications due to their structural stability and symmetry.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of a perfect cuboctahedron.

Total Surface Area of Cuboctahedron given Lateral Surface Area Calculator© - All Rights Reserved 2025