Total Surface Area of Spherical Segment Given Curved Surface Area Calculator

Formula Used:

\[ TSA = CSA + \pi \times (r_{Base}^2 + r_{Top}^2) \]

Curved Surface Area of Spherical Segment (CSA):

m²

Base Radius of Spherical Segment (rBase):

Top Radius of Spherical Segment (rTop):

Total Surface Area of Spherical Segment (TSA):

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1. What is Total Surface Area of Spherical Segment?

The Total Surface Area of a Spherical Segment is the quantity of plane enclosed on the entire surface of the Spherical Segment, including both the curved surface area and the areas of the top and bottom circular bases.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = CSA + \pi \times (r_{Base}^2 + r_{Top}^2) \]

Where:

\( TSA \) — Total Surface Area of Spherical Segment (m²)
\( CSA \) — Curved Surface Area of Spherical Segment (m²)
\( r_{Base} \) — Base Radius of Spherical Segment (m)
\( r_{Top} \) — Top Radius of Spherical Segment (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the total surface area by adding the curved surface area to the sum of the areas of the top and bottom circular bases.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various applications in geometry, engineering, and material science, such as determining the amount of material needed to cover a spherical segment or for heat transfer calculations.

4. Using the Calculator

Tips: Enter the curved surface area in square meters, base radius in meters, and top radius in meters. All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical segment?
A: A spherical segment is the solid defined by cutting a sphere with two parallel planes.

Q2: How is curved surface area different from total surface area?
A: Curved surface area includes only the lateral curved surface, while total surface area includes both the curved surface and the areas of the top and bottom circular bases.

Q3: Can this calculator handle different units?
A: The calculator uses meters and square meters. Convert all measurements to consistent units before calculation.

Q4: What if both radii are zero?
A: If both radii are zero, the spherical segment degenerates to a point, and the total surface area equals the curved surface area.

Q5: Are there limitations to this formula?
A: This formula assumes perfect spherical geometry and may not account for surface irregularities or deformations in real-world objects.