1. What is the Width of Cuboid Given Space Diagonal Formula?

The formula calculates the width of a cuboid when its space diagonal, length, and height are known. It is derived from the 3D Pythagorean theorem applied to the cuboid's dimensions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( w \) — Width of Cuboid (m)
• \( d_{Space} \) — Space Diagonal of Cuboid (m)
• \( l \) — Length of Cuboid (m)
• \( h \) — Height of Cuboid (m)

Explanation: The formula rearranges the 3D Pythagorean theorem \( d_{Space}^2 = l^2 + w^2 + h^2 \) to solve for width.

3. Importance of Width Calculation

Details: Calculating the width from known dimensions is essential in geometry, engineering, and construction for determining missing dimensions of cuboid-shaped objects.

4. Using the Calculator

Tips: Enter space diagonal, length, and height in meters. All values must be positive, and the space diagonal must be greater than the combination of length and height for a real solution.

5. Frequently Asked Questions (FAQ)

Q1: What if the calculated width is imaginary?
A: An imaginary result indicates that the given space diagonal is too short relative to the length and height, which is impossible for a real cuboid. Check your input values.

Q2: Can this formula be used for any unit of measurement?
A: Yes, as long as all dimensions are in the same unit. The calculator uses meters by default.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values. Rounding may occur in the displayed result.

Q4: What are common applications of this calculation?
A: Common in architecture, packaging design, and any field involving rectangular prism dimensions where one dimension needs to be derived.

Q5: Does the formula work for all cuboids?
A: Yes, it applies to all right cuboids (where all angles are right angles).