1. What is the Inner Radius of Hollow Hemisphere Formula?

The formula calculates the inner radius of a hollow hemisphere given its outer radius and volume. It's derived from the volume formula of a hollow hemisphere by solving for the inner radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{Inner} \) — Inner radius of hollow hemisphere (m)
• \( r_{Outer} \) — Outer radius of hollow hemisphere (m)
• \( V \) — Volume of hollow hemisphere (m³)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula rearranges the volume equation to solve for the inner radius, using the relationship between the volumes of the outer and inner hemispheres.

3. Importance of Inner Radius Calculation

Details: Calculating the inner radius is essential for determining the thickness of the hollow hemisphere, material requirements, and structural integrity analysis in engineering applications.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow hemisphere?
A: A hollow hemisphere is a three-dimensional shape formed by two concentric hemispheres with the same center but different radii.

Q2: What are the units for measurement?
A: The calculator uses meters for radius and cubic meters for volume. Ensure consistent units for accurate results.

Q3: Can this formula be used for any hollow hemisphere?
A: Yes, as long as the outer radius is greater than the inner radius and both are positive values.

Q4: What if the calculated inner radius is negative?
A: A negative result indicates invalid input values where the volume exceeds the maximum possible for the given outer radius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the volume formula, though practical measurements may have precision limitations.