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Face Area Of Cube Given Circumsphere Radius Calculator

Formula Used:

\[ \text{Face Area of Cube} = \frac{4}{3} \times (\text{Circumsphere Radius of Cube})^2 \]

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1. What is Face Area of Cube?

Face Area of Cube is the quantity of plane enclosed by any square face of the Cube. It represents the surface area of one face of the cube.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Face Area of Cube} = \frac{4}{3} \times (\text{Circumsphere Radius of Cube})^2 \]

Where:

Explanation: This formula calculates the area of one face of a cube using the radius of its circumsphere (the sphere that contains the cube with all vertices touching the sphere).

3. Importance of Face Area Calculation

Details: Calculating face area is important in geometry, architecture, and engineering for determining surface properties, material requirements, and structural analysis of cubic objects.

4. Using the Calculator

Tips: Enter the circumsphere radius in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumsphere radius?
A: Circumsphere radius is the radius of the sphere that contains the cube in such a way that all the vertices of the cube are touching the sphere.

Q2: How is face area different from total surface area?
A: Face area refers to the area of one face only, while total surface area is the sum of all six faces of the cube.

Q3: Can this formula be used for any cube?
A: Yes, this formula applies to all regular cubes where all sides are equal and all angles are right angles.

Q4: What are the practical applications of this calculation?
A: This calculation is used in packaging design, architectural planning, material estimation, and various engineering applications involving cubic structures.

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect cubes and provides precise results when accurate input values are provided.

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