Volume of Hollow Sphere Given Surface Area and Outer Radius Calculator

Formula Used:

\[ V = \frac{4}{3} \pi \left( r_{Outer}^3 - \left( \frac{SA}{4\pi} - r_{Outer}^2 \right)^{\frac{3}{2}} \right) \]

Volume of Hollow Sphere:

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1. What is the Volume of Hollow Sphere?

The Volume of Hollow Sphere is the total quantity of three dimensional space enclosed by the entire surface of the Hollow Sphere. It represents the space between the outer and inner spherical surfaces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{4}{3} \pi \left( r_{Outer}^3 - \left( \frac{SA}{4\pi} - r_{Outer}^2 \right)^{\frac{3}{2}} \right) \]

Where:

\( V \) — Volume of Hollow Sphere (m³)
\( r_{Outer} \) — Outer Radius of Hollow Sphere (m)
\( SA \) — Surface Area of Hollow Sphere (m²)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the volume by subtracting the volume of the inner sphere from the volume of the outer sphere, where the inner radius is derived from the given surface area.

3. Importance of Volume Calculation

Details: Calculating the volume of hollow spheres is crucial in various engineering and manufacturing applications, including pressure vessel design, storage tank capacity calculations, and architectural design of spherical structures.

4. Using the Calculator

Tips: Enter the outer radius in meters and surface area in square meters. Both values must be positive numbers. The calculator will compute the volume based on the mathematical relationship between these parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow sphere?
A: A hollow sphere is a three-dimensional geometric shape consisting of two concentric spheres with the same center but different radii, creating a hollow space between them.

Q2: How is the inner radius determined from surface area?
A: The surface area of a hollow sphere is given by \( SA = 4\pi(r_{Outer}^2 + r_{Inner}^2) \), which can be rearranged to solve for the inner radius.

Q3: What are typical applications of hollow spheres?
A: Hollow spheres are used in ball bearings, pressure vessels, architectural domes, sports equipment, and various mechanical components where weight reduction is important.

Q4: Are there limitations to this formula?
A: The formula assumes perfect spherical geometry and may not account for manufacturing tolerances or material thickness variations in real-world applications.

Q5: Can this calculator handle different units?
A: The calculator uses meters for radius and square meters for surface area. For other units, convert your measurements to these standard units before calculation.