Thickness of Hollow Sphere given Volume and Outer Radius Calculator

Formula Used:

\[ t = r_{Outer} - \left( r_{Outer}^3 - \frac{3V}{4\pi} \right)^{1/3} \]

Thickness of Hollow Sphere:

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1. What is the Thickness of Hollow Sphere Formula?

The thickness of a hollow sphere is calculated using the formula that relates the outer radius and volume of the sphere. This formula helps determine the distance between the inner and outer surfaces of a hollow spherical object.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = r_{Outer} - \left( r_{Outer}^3 - \frac{3V}{4\pi} \right)^{1/3} \]

Where:

\( t \) — Thickness of Hollow Sphere (m)
\( r_{Outer} \) — Outer Radius of Hollow Sphere (m)
\( V \) — Volume of Hollow Sphere (m³)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: The formula calculates the thickness by subtracting the inner radius (derived from the volume) from the outer radius of the hollow sphere.

3. Importance of Thickness Calculation

Details: Calculating the thickness of a hollow sphere is important in engineering and manufacturing for determining material requirements, structural integrity, and weight calculations of spherical containers and components.

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 thickness of the hollow sphere.

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 a hollow interior, creating a uniform thickness between the inner and outer surfaces.

Q2: Why is thickness important in hollow spheres?
A: Thickness determines the structural strength, weight, and material volume of the sphere, which are critical factors in design and engineering applications.

Q3: Can this formula be used for any hollow sphere?
A: Yes, this formula applies to any hollow sphere with a uniform thickness and known outer radius and volume.

Q4: What units should be used for input values?
A: The calculator uses meters for radius and cubic meters for volume. Ensure consistent units for accurate results.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. Accuracy depends on the precision of the measurements provided.