Inner Radius of Hollow Sphere Given Volume Calculator

Formula Used:

\[ r_{Inner} = (r_{Outer}^3 - \frac{3V}{4\pi})^{\frac{1}{3}} \]

Inner Radius of Hollow Sphere:

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1. What is Inner Radius of Hollow Sphere?

The inner radius of a hollow sphere is the distance from the center of the sphere to the inner surface. It defines the size of the empty cavity inside the hollow sphere and is a crucial parameter in determining the sphere's structural properties and volume.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Inner} = (r_{Outer}^3 - \frac{3V}{4\pi})^{\frac{1}{3}} \]

Where:

\( r_{Inner} \) — Inner radius of the hollow sphere (m)
\( r_{Outer} \) — Outer radius of the hollow sphere (m)
\( V \) — Volume of the hollow sphere (m³)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula is derived from the volume formula of a hollow sphere by solving for the inner radius.

3. Importance of Inner Radius Calculation

Details: Calculating the inner radius is essential for engineering applications, material science, and physics problems involving hollow spherical structures. It helps determine wall thickness, structural integrity, and material requirements.

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 inner radius based on the given inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow sphere?
A: A hollow sphere is a three-dimensional object with a spherical outer surface and an empty interior cavity, characterized by both outer and inner radii.

Q2: How is the volume of a hollow sphere calculated?
A: The volume is calculated as \( V = \frac{4}{3}\pi(r_{Outer}^3 - r_{Inner}^3) \), which is the difference between the volumes of the outer and inner spheres.

Q3: What are typical applications of hollow spheres?
A: Hollow spheres are used in various applications including pressure vessels, buoyancy devices, architectural structures, and mechanical components.

Q4: Are there limitations to this formula?
A: The formula assumes perfect spherical geometry and uniform wall thickness. It may not be accurate for irregular shapes or non-uniform materials.

Q5: Can this calculator handle different units?
A: The calculator uses meters for radius and cubic meters for volume. Convert other units to these standard SI units before calculation.