1. What is the Total Surface Area of Paraboloid?

The Total Surface Area of a Paraboloid is the sum of its lateral surface area and the area of its circular base. It represents the total two-dimensional space enclosed on the entire surface of the paraboloid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The formula calculates the total surface area by adding the lateral curved surface area to the area of the circular base of the paraboloid.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area of a paraboloid is important in various engineering and architectural applications, including structural design, material estimation, and fluid dynamics calculations.

4. Using the Calculator

Tips: Enter the lateral surface area in square meters and the radius in meters. Both values must be non-negative numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a paraboloid?
A: A paraboloid is a quadratic surface that can be generated by rotating a parabola around its axis of symmetry.

Q2: How is lateral surface area different from total surface area?
A: Lateral surface area includes only the curved surface, while total surface area includes both the curved surface and the base area.

Q3: What are practical applications of paraboloids?
A: Paraboloids are used in satellite dishes, headlights, telescopes, and architectural structures due to their reflective properties.

Q4: Can this calculator handle different units?
A: The calculator uses meters and square meters. Convert other units to these before calculation.

Q5: Is the formula applicable to all types of paraboloids?
A: This formula applies to circular paraboloids where the base is a perfect circle.