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Space Diagonal of Cuboid Formula:
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The space diagonal of a cuboid is the longest straight line that can be drawn from one corner of the cuboid to the opposite corner, passing through the interior of the cuboid. It connects two vertices that are not on the same face.
The calculator uses the space diagonal formula derived from total surface area:
Where:
Explanation: The formula first calculates the width using the surface area formula, then applies the Pythagorean theorem in three dimensions to find the space diagonal.
Details: Calculating the space diagonal is important in geometry, architecture, and engineering for determining the maximum distance between opposite corners of a rectangular prism, which is crucial for structural design and spatial planning.
Tips: Enter the total surface area, length, and height of the cuboid. All values must be positive numbers. The calculator will compute the space diagonal using the derived formula.
Q1: What is the difference between space diagonal and face diagonal?
A: Space diagonal connects opposite corners through the 3D space of the cuboid, while face diagonal lies on one face of the cuboid and connects opposite corners of that face.
Q2: Can the space diagonal be longer than the sum of the edges?
A: Yes, the space diagonal is typically longer than any single edge and follows the Pythagorean theorem in three dimensions.
Q3: What units should I use for the inputs?
A: Use consistent units for all measurements (e.g., all in meters, centimeters, or inches). The result will be in the same unit.
Q4: What if I get a negative value for width?
A: A negative width indicates invalid input values that don't form a valid cuboid. Please check your input values.
Q5: Can this formula be used for cubes?
A: Yes, a cube is a special case of a cuboid where all edges are equal. The formula simplifies for cubes.