Surface Area of Hollow Sphere given Surface to Volume Ratio Calculator

Surface Area of Hollow Sphere Formula:

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

Surface Area of Hollow Sphere (SA):

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1. What is the Surface Area of Hollow Sphere?

The Surface Area of a Hollow Sphere is the total quantity of two dimensional space enclosed by the spherical surface. It represents the area of both the outer and inner surfaces combined.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( SA \) — Surface Area of Hollow Sphere (m²)
\( \pi \) — Archimedes' constant (≈3.14159)
\( \frac{RA}{V} \) — Surface to Volume Ratio (1/m)
\( r_{Outer} \) — Outer Radius of Hollow Sphere (m)
\( r_{Inner} \) — Inner Radius of Hollow Sphere (m)

Explanation: The formula calculates the surface area based on the surface to volume ratio and the difference between the cubes of outer and inner radii.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of hollow spheres is crucial in various engineering applications, material science, heat transfer calculations, and architectural designs involving spherical structures.

4. Using the Calculator

Tips: Enter surface to volume ratio in 1/m, outer and inner radii in meters. All values must be positive, and outer radius must be greater than inner radius.

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 spherical cavity inside, creating a uniform thickness throughout.

Q2: Why is surface to volume ratio important?
A: Surface to volume ratio is crucial in determining various physical properties including heat transfer rates, chemical reaction rates, and material strength.

Q3: What are typical applications of hollow spheres?
A: Hollow spheres are used in pressure vessels, storage tanks, architectural domes, sports equipment, and various engineering components.

Q4: How does wall thickness affect surface area?
A: For a given outer radius, thicker walls (smaller inner radius) result in greater surface area due to the additional inner surface area.

Q5: Can this formula be used for other shapes?
A: No, this specific formula is designed for hollow spheres. Other geometric shapes have different surface area formulas.