Thickness of Hollow Sphere given Surface Area and Inner Radius Calculator

Formula Used:

\[ t = \sqrt{\frac{SA}{4\pi} - r_{Inner}^2} - r_{Inner} \]

Thickness of Hollow Sphere (t):

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1. What is the Thickness of Hollow Sphere Formula?

The thickness of a hollow sphere can be calculated using the surface area and inner radius. 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:

\[ t = \sqrt{\frac{SA}{4\pi} - r_{Inner}^2} - r_{Inner} \]

Where:

\( t \) — Thickness of Hollow Sphere (m)
\( SA \) — Surface Area of Hollow Sphere (m²)
\( r_{Inner} \) — Inner Radius of Hollow Sphere (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives from the relationship between surface area, inner radius, and thickness of a hollow sphere.

3. Importance of Thickness Calculation

Details: Calculating thickness is crucial for engineering applications, material strength analysis, and structural design of hollow spherical objects.

4. Using the Calculator

Tips: Enter surface area in square meters and inner radius in meters. Both values must be positive numbers.

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 inner cavity.

Q2: Can this formula be used for any hollow sphere?
A: Yes, this formula applies to any perfect hollow sphere with uniform thickness.

Q3: What are the units for thickness?
A: Thickness is typically measured in meters (m) or appropriate length units.

Q4: What if the calculated thickness is negative?
A: A negative result indicates invalid input values where the inner radius is too large for the given surface area.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect geometric spheres with uniform thickness.