Volume Of Hollow Hemisphere Given Total Surface Area And Outer Radius Calculator

Volume Of Hollow Hemisphere Given Total Surface Area And Outer Radius Formula:

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

Volume Of Hollow Hemisphere:

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1. What Is The Volume Of Hollow Hemisphere Given Total Surface Area And Outer Radius?

The Volume Of Hollow Hemisphere Given Total Surface Area And Outer Radius is the measure of three-dimensional space enclosed by all the faces of the Hollow Hemisphere, calculated using the outer radius and total surface area.

2. How Does The Calculator Work?

The calculator uses the formula:

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

Where:

\( V \) — Volume of Hollow Hemisphere (m³)
\( r_{Outer} \) — Outer Radius of Hollow Hemisphere (m)
\( TSA \) — Total Surface Area of Hollow Hemisphere (m²)
\( \pi \) — Archimedes' constant (approximately 3.1416)

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

3. Importance Of Volume Calculation

Details: Accurate volume calculation is crucial for determining the capacity of hollow hemispherical objects, material requirements, and structural analysis in engineering and design applications.

4. Using The Calculator

Tips: Enter outer radius in meters, total surface area in square meters. All values must be valid (radius > 0, surface area > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow hemisphere?
A: A hollow hemisphere is a three-dimensional shape that resembles a half-sphere with a hollow interior, consisting of an outer and inner hemispherical surface.

Q2: How is this formula derived?
A: The formula is derived by calculating the difference between the volumes of the outer and inner hemispheres, where the inner radius is determined from the total surface area equation.

Q3: What are the units of measurement?
A: The calculator uses meters for radius and square meters for surface area, resulting in cubic meters for volume. Consistent units must be maintained.

Q4: Are there limitations to this calculation?
A: The formula assumes perfect hemispherical geometry and may not be accurate for irregular shapes or when the inner radius cannot be realistically determined from the given parameters.

Q5: Can this calculator handle different units?
A: The calculator requires inputs in meters and square meters. For other units, convert values to these standard units before calculation.