1. What is the Height of Cuboid given Space Diagonal Formula?

The formula calculates the height of a cuboid when its space diagonal, length, and width are known. It is derived from the Pythagorean theorem applied in three dimensions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The formula calculates the height by subtracting the squares of length and width from the square of the space diagonal, then taking the square root of the result.

3. Importance of Height Calculation

Details: Calculating the height of a cuboid is essential in geometry, architecture, and engineering for determining volume, surface area, and spatial relationships in three-dimensional objects.

4. Using the Calculator

Tips: Enter space diagonal, length, and width in meters. All values must be positive numbers, and the space diagonal must be greater than the square root of the sum of squares of length and width for a valid result.

5. Frequently Asked Questions (FAQ)

Q1: What is a cuboid?
A: A cuboid is a three-dimensional shape with six rectangular faces, where opposite faces are equal and parallel.

Q2: What is the space diagonal of a cuboid?
A: The space diagonal is the longest straight line that can be drawn from one vertex to the opposite vertex through the interior of the cuboid.

Q3: Can this formula be used for any rectangular prism?
A: Yes, since a cuboid is a type of rectangular prism, this formula applies to all rectangular prisms.

Q4: What units should be used for input values?
A: The calculator uses meters, but any consistent unit of length can be used as long as all inputs are in the same unit.

Q5: What if the result is imaginary?
A: An imaginary result indicates that the input values are inconsistent (space diagonal squared is less than the sum of length squared and width squared), which is impossible for a real cuboid.