Surface To Volume Ratio Of Hollow Sphere Given Surface Area And Outer Radius Calculator

Formula Used:

\[ \text{Surface to Volume Ratio} = 3 \times \frac{\frac{SA}{4\pi}}{r_{\text{Outer}}^3 - \left(\frac{SA}{4\pi} - r_{\text{Outer}}^2\right)^{3/2}} \]

Surface to Volume Ratio:

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1. What is Surface to Volume Ratio of Hollow Sphere?

The Surface to Volume Ratio of a Hollow Sphere is the numerical ratio of the total surface area to the volume of the hollow sphere. It's an important geometric property that indicates how much surface area is available per unit volume.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Surface to Volume Ratio} = 3 \times \frac{\frac{SA}{4\pi}}{r_{\text{Outer}}^3 - \left(\frac{SA}{4\pi} - r_{\text{Outer}}^2\right)^{3/2}} \]

Where:

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

Explanation: The formula calculates the surface to volume ratio based on the given surface area and outer radius of the hollow sphere.

3. Importance of Surface to Volume Ratio

Details: The surface to volume ratio is crucial in various fields including materials science, chemistry, and physics. It affects properties like heat transfer, chemical reactivity, and diffusion rates in hollow spherical structures.

4. Using the Calculator

Tips: Enter the surface area in square meters and outer radius in meters. Both values must be positive numbers. The calculator will compute the surface to volume ratio in per meter units.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for surface to volume ratio?
A: The ratio varies significantly based on the dimensions of the hollow sphere. Smaller spheres generally have higher surface to volume ratios.

Q2: How does wall thickness affect the ratio?
A: Thinner walls generally result in higher surface to volume ratios as more volume is contained within the same surface area.

Q3: Can this formula be used for solid spheres?
A: No, this formula is specifically designed for hollow spheres. Solid spheres have a different surface to volume ratio calculation.

Q4: What are practical applications of this calculation?
A: This calculation is important in designing spherical containers, chemical reactors, and understanding biological cell structures.

Q5: Are there limitations to this formula?
A: The formula assumes perfect spherical geometry and may not account for surface irregularities or non-uniform wall thickness.