Inner Height of Obtuse Edged Cuboid given Space Diagonal Calculator

Formula Used:

\[ h_{Inner} = \sqrt{(d_{Space} - 2 \times \sqrt{\frac{w_{Cut}^2}{6}})^2 - w_{Inner}^2 - l_{Inner}^2} \]

Space Diagonal of Obtuse Edged Cuboid:

Cut Width of Obtuse Edged Cuboid:

Inner Width of Obtuse Edged Cuboid:

Inner Length of Obtuse Edged Cuboid:

Inner Height of Obtuse Edged Cuboid:

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1. What is the Inner Height of Obtuse Edged Cuboid?

The Inner Height of Obtuse Edged Cuboid is the height of the smaller cuboid formed after edges are regularly cut off from the original cuboid to form the Obtuse Edged Cuboid. It represents the vertical dimension of the inner structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_{Inner} = \sqrt{(d_{Space} - 2 \times \sqrt{\frac{w_{Cut}^2}{6}})^2 - w_{Inner}^2 - l_{Inner}^2} \]

Where:

\( h_{Inner} \) — Inner Height of Obtuse Edged Cuboid (m)
\( d_{Space} \) — Space Diagonal of Obtuse Edged Cuboid (m)
\( w_{Cut} \) — Cut Width of Obtuse Edged Cuboid (m)
\( w_{Inner} \) — Inner Width of Obtuse Edged Cuboid (m)
\( l_{Inner} \) — Inner Length of Obtuse Edged Cuboid (m)

Explanation: The formula calculates the inner height by considering the space diagonal, cut width, inner width, and inner length of the obtuse edged cuboid.

3. Importance of Inner Height Calculation

Details: Calculating the inner height is crucial for understanding the dimensional properties of obtuse edged cuboids, which are important in various engineering and architectural applications where precise measurements are required.

4. Using the Calculator

Tips: Enter all values in meters. Space diagonal, cut width, inner width, and inner length must be positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is an Obtuse Edged Cuboid?
A: An Obtuse Edged Cuboid is a three-dimensional shape formed by cutting off the edges of a regular cuboid, resulting in a polyhedron with obtuse angles at the edges.

Q2: Why is the cut width squared and divided by 6 in the formula?
A: This term accounts for the geometric relationship between the cut width and the space diagonal, ensuring accurate calculation of the inner dimensions.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit. For other units, convert all measurements to meters before inputting them into the calculator.

Q4: What if I get a negative value under the square root?
A: A negative value indicates that the input values are inconsistent with a valid obtuse edged cuboid. Please verify your measurements.

Q5: How precise are the calculations?
A: The calculator provides results with up to 6 decimal places for high precision, suitable for most engineering applications.