Radius of Paraboloid given Total Surface Area and Lateral Surface Area Calculator

Formula Used:

\[ r = \sqrt{\frac{TSA - LSA}{\pi}} \]

Radius of Paraboloid:

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1. What is the Radius of Paraboloid Formula?

The formula calculates the radius of a paraboloid given its total surface area and lateral surface area. It provides a mathematical relationship between these geometric properties of a paraboloid shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \sqrt{\frac{TSA - LSA}{\pi}} \]

Where:

\( r \) — Radius of Paraboloid (m)
\( TSA \) — Total Surface Area of Paraboloid (m²)
\( LSA \) — Lateral Surface Area of Paraboloid (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives from the geometric relationship between total surface area, lateral surface area, and the base area of the paraboloid.

3. Importance of Radius Calculation

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

4. Using the Calculator

Tips: Enter total surface area and lateral surface area in square meters. Both values must be positive numbers, and total surface area must be greater than lateral surface area.

5. Frequently Asked Questions (FAQ)

Q1: What is a paraboloid?
A: A paraboloid is a quadratic surface that resembles a parabola in three dimensions. It can be elliptic or hyperbolic in nature.

Q2: Why is π used in the formula?
A: π is used because the base of a paraboloid is circular, and the formula involves calculating the area of this circular base.

Q3: What are typical applications of paraboloids?
A: Paraboloids are commonly used in satellite dishes, headlight reflectors, telescope mirrors, and architectural designs.

Q4: What units should I use for the inputs?
A: The calculator uses square meters for area measurements, but you can use any consistent unit system as long as both area values use the same units.

Q5: What if TSA is not greater than LSA?
A: Total surface area must always be greater than lateral surface area since it includes both lateral surface area and the base area. If TSA ≤ LSA, the input values are invalid.