Inner Radius of Hollow Sphere given Surface Area Calculator

Formula Used:

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

Inner Radius of Hollow Sphere (r_Inner):

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1. What is the Inner Radius of Hollow Sphere Formula?

The formula calculates the inner radius of a hollow sphere given its surface area and outer radius. It's derived from the surface area formula of a hollow sphere and provides an accurate measurement of the inner dimension.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( r_{Inner} \) — Inner radius of hollow sphere (m)
\( SA \) — Surface area of hollow sphere (m²)
\( r_{Outer} \) — Outer radius of hollow sphere (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula rearranges the surface area equation of a hollow sphere to solve for the inner radius, using the given surface area and outer radius values.

3. Importance of Inner Radius Calculation

Details: Calculating the inner radius is crucial for determining the volume of hollow space, material thickness, and structural properties of hollow spherical objects in engineering and design applications.

4. Using the Calculator

Tips: Enter surface area in square meters and outer radius in meters. Both values must be positive numbers. The calculator will compute the inner radius automatically.

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 an empty interior, characterized by both inner and outer radii.

Q2: What are the units used in this calculation?
A: The formula uses consistent units - meters for radii and square meters for surface area. Ensure all inputs use the same unit system.

Q3: When is this calculation invalid?
A: The calculation is invalid when the outer radius squared is greater than SA/(4π), which would result in a negative value under the square root.

Q4: Can this formula be used for other shapes?
A: No, this specific formula applies only to hollow spheres. Other geometric shapes have different formulas for calculating inner dimensions.

Q5: What are practical applications of this calculation?
A: This calculation is used in engineering design, architecture, manufacturing, and physics for designing pressure vessels, storage tanks, and structural components.