1. What is the Radius of Paraboloid Formula?

The formula calculates the radius of a paraboloid given its volume and height. It's derived from the volume formula of a paraboloid and solved for the radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of Paraboloid (m)
• \( V \) — Volume of Paraboloid (m³)
• \( h \) — Height of Paraboloid (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula rearranges the volume equation \( V = \frac{1}{2}\pi r^2 h \) to solve for the radius \( r \).

3. Importance of Radius Calculation

Details: Calculating the radius of a paraboloid is essential in various engineering and architectural applications where parabolic shapes are used, such as satellite dishes, reflectors, and structural designs.

4. Using the Calculator

Tips: Enter the volume in cubic meters and height in meters. Both values must be positive numbers. The calculator will compute the radius in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is a paraboloid?
A: A paraboloid is a quadratic surface that resembles a parabola in three dimensions. Common examples include satellite dishes and parabolic reflectors.

Q2: Why is the formula structured this way?
A: The formula is derived from the volume formula of a paraboloid \( V = \frac{1}{2}\pi r^2 h \), rearranged to solve for radius \( r \).

Q3: What units should I use?
A: The calculator uses meters for both input and output. Ensure consistent units for accurate results.

Q4: Can this formula be used for any paraboloid?
A: Yes, this formula applies to all right circular paraboloids where the cross-section is circular.

Q5: What if I have diameter instead of radius?
A: The radius is half the diameter. You can calculate diameter by multiplying the radius by 2.