Volume of Spherical Sector given Total Surface Area and Spherical Cap Height Calculator

Formula Used:

\[ V = 2\pi \left( \frac{TSA}{\pi((2h_{Cap}) + r_{Cap})} \right)^2 \frac{h_{Cap}}{3} \]

Total Surface Area of Spherical Sector (TSA):

m²

Spherical Cap Height of Spherical Sector (hCap):

Spherical Cap Radius of Spherical Sector (rCap):

Volume of Spherical Sector (V):

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1. What is the Volume of Spherical Sector?

The Volume of Spherical Sector is the amount of three dimensional space occupied by the Spherical Sector. It represents the total capacity enclosed within the boundaries of the spherical sector.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = 2\pi \left( \frac{TSA}{\pi((2h_{Cap}) + r_{Cap})} \right)^2 \frac{h_{Cap}}{3} \]

Where:

\( V \) — Volume of Spherical Sector (m³)
\( TSA \) — Total Surface Area of Spherical Sector (m²)
\( h_{Cap} \) — Spherical Cap Height of Spherical Sector (m)
\( r_{Cap} \) — Spherical Cap Radius of Spherical Sector (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the volume of a spherical sector based on its total surface area and the dimensions of its spherical cap.

3. Importance of Volume Calculation

Details: Calculating the volume of a spherical sector is important in various engineering, architectural, and mathematical applications where precise volume measurements of spherical segments are required.

4. Using the Calculator

Tips: Enter total surface area in square meters, spherical cap height in meters, and spherical cap radius in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical sector?
A: A spherical sector is a portion of a sphere defined by a conical boundary with apex at the sphere's center and a spherical cap on the surface.

Q2: How is this different from a spherical cap volume?
A: A spherical sector includes both the spherical cap and the conical section that connects it to the sphere's center, while a spherical cap only includes the curved surface portion.

Q3: What are practical applications of this calculation?
A: This calculation is used in tank design, architectural domes, planetary science, and any application involving spherical containers or structures.

Q4: Are there limitations to this formula?
A: The formula assumes perfect spherical geometry and may not be accurate for irregular or deformed spherical shapes.

Q5: Can this calculator handle different units?
A: The calculator uses meters for all linear measurements and square meters for area. Convert other units to meters before inputting values.