1. What is Space Diagonal of Cuboid?

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.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Space diagonal of the cuboid
• \( TSA \) — Total surface area of the cuboid
• \( l \) — Length of the cuboid
• \( w \) — Width of the cuboid

Explanation: The formula first calculates the height of the cuboid from the given TSA, length, and width, then applies the 3D Pythagorean theorem to find the space diagonal.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is important in various applications including packaging design, construction, 3D modeling, and determining the maximum length of objects that can fit inside containers or boxes.

4. Using the Calculator

Tips: Enter the total surface area in square meters, length in meters, and width in meters. All values must be positive numbers. The calculator will compute the space diagonal automatically.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between space diagonal and face diagonal?
A: Space diagonal connects opposite corners through the 3D space, while face diagonal lies on one face of the cuboid and connects opposite corners of that face.

Q2: Can this formula be used for cubes?
A: Yes, for cubes where length = width = height, the formula simplifies to \( d = l\sqrt{3} \).

Q3: What units should I use for the inputs?
A: Use consistent units (e.g., all in meters). The result will be in the same linear unit.

Q4: What if I get a negative value under the square root?
A: This indicates invalid input values where the given TSA is too small for the specified length and width dimensions.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cuboids with the given dimensions.