Base Radius Of Circular Hyperboloid Given Volume Calculator

Formula Used:

\[ r_{Base} = \sqrt{\frac{3V}{\pi h} - 2r_{Skirt}^2} \]

Volume of Circular Hyperboloid (V):

m³

Height of Circular Hyperboloid (h):

Skirt Radius of Circular Hyperboloid (r_Skirt):

Base Radius of Circular Hyperboloid (r_Base):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Base Radius of Circular Hyperboloid?

The Base Radius of a Circular Hyperboloid is the distance from the center to any point on the circumference of the circular face at the bottom of the hyperboloid. It is a fundamental geometric parameter that helps define the shape and size of the hyperboloid structure.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ r_{Base} = \sqrt{\frac{3V}{\pi h} - 2r_{Skirt}^2} \]

Where:

\( r_{Base} \) — Base Radius of Circular Hyperboloid (m)
\( V \) — Volume of Circular Hyperboloid (m³)
\( h \) — Height of Circular Hyperboloid (m)
\( r_{Skirt} \) — Skirt Radius of Circular Hyperboloid (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula derives from the geometric properties of a circular hyperboloid, relating the base radius to the volume, height, and skirt radius of the structure.

3. Importance of Base Radius Calculation

Details: Calculating the base radius is essential for architectural design, structural engineering, and manufacturing processes involving hyperboloid shapes. It helps determine the stability, material requirements, and overall dimensions of the structure.

4. Using the Calculator

Tips: Enter the volume in cubic meters, height in meters, and skirt radius in meters. All values must be positive numbers (volume > 0, height > 0, skirt radius ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a Circular Hyperboloid?
A: A Circular Hyperboloid is a three-dimensional surface generated by rotating a hyperbola around one of its principal axes, creating a structure with circular cross-sections.

Q2: What is the Skirt Radius?
A: The Skirt Radius is the distance from center to any point on the circumference of the smallest circular cross-section when cutting the hyperboloid by a horizontal plane.

Q3: Can this formula be used for any hyperboloid?
A: This specific formula applies to circular hyperboloids of one sheet where the base and top are circular and parallel.

Q4: What if the calculated base radius is imaginary?
A: An imaginary result indicates that the input values are not physically possible for a circular hyperboloid. Please verify your inputs.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the geometric properties of circular hyperboloids, assuming perfect geometric shapes.