Total Surface Area Of Spherical Sector Given Volume Calculator

Formula Used:

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

Spherical Radius of Spherical Sector:

Volume of Spherical Sector:

m³

Spherical Cap Radius of Spherical Sector:

Total Surface Area of Spherical Sector:

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1. What is the Total Surface Area of Spherical Sector?

The Total Surface Area of Spherical Sector is defined as the total quantity of two-dimensional space enclosed on the entire surface of the Spherical Sector, including both the curved surface and the base area.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the total surface area by considering the relationship between the volume, spherical radius, and cap radius of the spherical sector.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area of a spherical sector is important in various engineering, architectural, and mathematical applications where surface coverage, material requirements, or heat transfer calculations are needed for spherical segments.

4. Using the Calculator

Tips: Enter the spherical radius in meters, volume in cubic meters, and spherical cap radius in meters. All values must be positive numbers (spherical cap radius can be zero for a hemisphere).

5. Frequently Asked Questions (FAQ)

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

Q2: Can the spherical cap radius be zero?
A: Yes, when the spherical cap radius is zero, the spherical sector becomes a full sphere, and the formula calculates the total surface area of a sphere.

Q3: What are the units for the inputs and outputs?
A: The calculator uses meters for length inputs, cubic meters for volume, and square meters for the surface area result.

Q4: How accurate is the calculation?
A: The calculation uses the precise mathematical formula and provides results with high accuracy based on the input values.

Q5: Can this calculator be used for educational purposes?
A: Yes, this calculator is an excellent tool for students and educators to understand and verify calculations related to spherical geometry and surface area computations.