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Total Surface Area of Cube is the quantity of plane enclosed by the entire surface of the Cube. The insphere radius of a cube is the radius of the sphere that is contained by the Cube in such a way that all the faces just touching the sphere.
The calculator uses the formula:
Where:
Explanation: This formula calculates the total surface area of a cube based on the radius of its inscribed sphere.
Details: Calculating the total surface area of a cube is important in various engineering, architectural, and mathematical applications where surface coverage, material requirements, or heat transfer calculations are needed.
Tips: Enter the insphere radius in meters. The value must be valid (radius > 0).
Q1: What is the relationship between insphere radius and cube side length?
A: The insphere radius of a cube is equal to half of the cube's side length (\( r_i = a/2 \)).
Q2: How is this formula derived?
A: The formula is derived from the relationship between the cube's surface area (\( 6a^2 \)) and the insphere radius (\( r_i = a/2 \)), resulting in \( TSA = 24r_i^2 \).
Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert your measurement to meters first or adjust the result accordingly.
Q4: What are typical values for insphere radius?
A: Typical values depend on the cube's size. For a standard 1m cube, the insphere radius would be 0.5m.
Q5: Is this formula applicable to all cubes?
A: Yes, this formula applies to all perfect cubes where all sides are equal and all angles are right angles.