1. What is Total Surface Area of Cube given Face Diagonal?

The Total Surface Area of a Cube given Face Diagonal is the total quantity of plane enclosed by the entire surface of the Cube, calculated using the face diagonal measurement.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( TSA \) — Total Surface Area of Cube (m²)
• \( dFace \) — Face Diagonal of Cube (m)

Explanation: The formula calculates the total surface area by multiplying the square of the face diagonal by 3.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area of a cube is important in various engineering, architectural, and mathematical applications where surface coverage or material requirements need to be determined.

4. Using the Calculator

Tips: Enter the face diagonal of the cube in meters. The value must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between face diagonal and total surface area?
A: The total surface area is directly proportional to the square of the face diagonal, multiplied by 3.

Q2: Can this formula be used for other 3D shapes?
A: No, this specific formula applies only to cubes where all faces are equal squares.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact when the input values are precise.

Q4: What units should be used for the face diagonal?
A: The face diagonal should be in meters, and the result will be in square meters. Consistent units must be maintained.

Q5: How does face diagonal relate to edge length?
A: Face diagonal = edge length × √2. This relationship can be used to convert between different measurements.