1. What is the Radius of Hemisphere Calculation?

The radius of a hemisphere is calculated from its total surface area using the mathematical relationship between these two geometric properties. This calculation is essential in various engineering and architectural applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of the hemisphere (m)
• \( TSA \) — Total surface area of the hemisphere (m²)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula derives from the total surface area formula of a hemisphere and solves for the radius.

3. Importance of Radius Calculation

Details: Calculating the radius from surface area is crucial for designing hemispherical structures, manufacturing spherical components, and solving geometric problems in mathematics and physics.

4. Using the Calculator

Tips: Enter the total surface area in square meters. The value must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between radius and surface area?
A: The surface area of a hemisphere is proportional to the square of its radius, following the formula TSA = 3πr².

Q2: Can this calculator be used for full spheres?
A: No, this calculator is specifically designed for hemispheres. For full spheres, the surface area formula is 4πr².

Q3: What units should I use?
A: The calculator uses meters for radius and square meters for surface area. Ensure consistent units for accurate results.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, provided the input surface area is accurate and the hemisphere is perfectly shaped.

Q5: What if I have the curved surface area instead of total surface area?
A: For curved surface area (2πr²), you would need to use a different formula: r = √(CSA/2π).