Total Surface Area Of Spherical Sector Given Surface To Volume Ratio And Spherical Cap Radius Calculator

Formula Used:

\[ TSA = \frac{3\pi(2h_{Cap} + r_{Cap})^2}{2h_{Cap} \cdot R_{A/V}} \]

Spherical Cap Height of Spherical Sector (hCap):

Spherical Cap Radius of Spherical Sector (rCap):

Surface to Volume Ratio of Spherical Sector (RA/V):

1/m

Total Surface Area of Spherical Sector (TSA):

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1. What is Total Surface Area of Spherical Sector?

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:

\[ TSA = \frac{3\pi(2h_{Cap} + r_{Cap})^2}{2h_{Cap} \cdot R_{A/V}} \]

Where:

\( TSA \) — 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)
\( R_{A/V} \) — Surface to Volume Ratio of Spherical Sector (1/m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the total surface area of a spherical sector based on the cap height, cap radius, and the surface to volume ratio of the sector.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area of a spherical sector is important in various engineering and architectural applications, particularly in designing domed structures, storage tanks, and other spherical components where surface area affects material requirements, heat transfer, and structural integrity.

4. Using the Calculator

Tips: Enter the spherical cap height and radius in meters, and the surface to volume ratio in 1/m. All values must be positive numbers (height > 0, ratio > 0, radius ≥ 0).

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 the apex at the sphere's center and the base on the sphere's surface.

Q2: How is this different from a spherical cap?
A: A spherical sector includes both the curved surface area and the base area, while a spherical cap typically refers to just the curved surface portion.

Q3: What are typical applications of this calculation?
A: This calculation is used in architectural design, tank manufacturing, aerospace engineering, and any application involving spherical or dome-shaped structures.

Q4: What units should I use for input values?
A: Use meters for length measurements (hCap, rCap) and 1/m for the surface to volume ratio. The result will be in square meters.

Q5: Can this formula be used for any spherical sector?
A: This specific formula applies when you have the cap height, cap radius, and surface to volume ratio. Different formulas may be needed if other parameters are known.