Volume Of Obelisk Given Frustum Height And Height Of Obelisk Calculator

Formula Used:

\[ V = \frac{h_{Frustum} \times (l_{Base}^2 + l_{Transition}^2 + \sqrt{l_{Base}^2 \times l_{Transition}^2}) + l_{Transition}^2 \times (h - h_{Frustum})}{3} \]

Frustum Height of Obelisk:

Base Edge Length of Obelisk:

Transition Edge Length of Obelisk:

Height of Obelisk:

Volume of Obelisk:

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1. What is the Volume of Obelisk Formula?

The volume of an obelisk is calculated using a formula that combines the volume of the frustum (truncated pyramid) section and the pyramid section. This formula provides an accurate measurement of the total three-dimensional space enclosed by the obelisk's surface.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{h_{Frustum} \times (l_{Base}^2 + l_{Transition}^2 + \sqrt{l_{Base}^2 \times l_{Transition}^2}) + l_{Transition}^2 \times (h - h_{Frustum})}{3} \]

Where:

\( V \) — Volume of Obelisk (m³)
\( h_{Frustum} \) — Frustum Height of Obelisk (m)
\( l_{Base} \) — Base Edge Length of Obelisk (m)
\( l_{Transition} \) — Transition Edge Length of Obelisk (m)
\( h \) — Height of Obelisk (m)

Explanation: The formula calculates the combined volume of the frustum section and the pyramid section of the obelisk, providing the total volume.

3. Importance of Volume Calculation

Details: Accurate volume calculation is crucial for architectural design, material estimation, structural analysis, and historical preservation of obelisk structures.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure that the height of obelisk is greater than the frustum height. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is an obelisk?
A: An obelisk is a tall, four-sided, narrow tapering monument which ends in a pyramid-like shape at the top.

Q2: Why is the formula divided by 3?
A: The division by 3 comes from the volume formula for pyramids and cones, which is (base area × height)/3.

Q3: What units should I use for the inputs?
A: The calculator uses meters for all measurements, but you can use any consistent unit as long as all inputs are in the same unit.

Q4: Can this calculator be used for other pyramid-like structures?
A: This specific formula is designed for obelisks with square bases. For other pyramid structures, different formulas may be needed.

Q5: What if my obelisk has a rectangular base instead of square?
A: This calculator assumes square bases. For rectangular bases, a different formula would be required to calculate the volume accurately.