Space Diagonal of Square Pillar given Volume Calculator

Space Diagonal Formula:

\[ d_{Space} = \sqrt{(2 \times B_{Edges}^2) + \left(\frac{V}{B_{Edges}^2}\right)^2} \]

Space Diagonal of Square Pillar (d_Space):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Space Diagonal of Square Pillar?

The Space Diagonal of a Square Pillar is a straight line connecting two vertices that are not on the same face of the Square Pillar. It passes through the interior of the pillar and represents the longest distance between any two points in the three-dimensional structure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Space} = \sqrt{(2 \times B_{Edges}^2) + \left(\frac{V}{B_{Edges}^2}\right)^2} \]

Where:

\( d_{Space} \) — Space Diagonal of Square Pillar (m)
\( B_{Edges} \) — Base Edges of Square Pillar (m)
\( V \) — Volume of Square Pillar (m³)

Explanation: The formula calculates the space diagonal by combining the base diagonal and the height of the pillar using the Pythagorean theorem in three dimensions.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is important in structural engineering, architecture, and 3D modeling. It helps determine the maximum length of objects that can fit inside the pillar or pass through it diagonally.

4. Using the Calculator

Tips: Enter the base edge length in meters and volume in cubic meters. Both values must be positive numbers. The calculator will compute the space diagonal using the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between space diagonal and face diagonal?
A: Space diagonal connects two non-adjacent vertices through the 3D interior, while face diagonal lies on a single face of the pillar.

Q2: Can this formula be used for rectangular pillars?
A: No, this specific formula is designed for square pillars where all base edges are equal. For rectangular pillars, a different formula is needed.

Q3: What are the units of measurement for the space diagonal?
A: The space diagonal is measured in the same units as the base edges (typically meters or feet).

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect square pillars, assuming precise input values.

Q5: Can I calculate the space diagonal if I know the height instead of volume?
A: Yes, with height (h), the formula becomes: \( d_{Space} = \sqrt{(2 \times B_{Edges}^2) + h^2} \)