Curved Surface Area of Spherical Segment given Total Surface Area Calculator

Formula Used:

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

Total Surface Area of Spherical Segment (TSA):

m²

Base Radius of Spherical Segment:

Top Radius of Spherical Segment:

Curved Surface Area of Spherical Segment (CSA):

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1. What is the Curved Surface Area of Spherical Segment?

The Curved Surface Area of a Spherical Segment refers to the area of the curved surface portion of a spherical segment, excluding the top and bottom circular bases. It represents the lateral surface area of the segment cut from a sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( CSA \) — Curved Surface Area of Spherical Segment (m²)
\( TSA \) — Total 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: This formula calculates the curved surface area by subtracting the combined area of the top and bottom circular bases from the total surface area of the spherical segment.

3. Importance of CSA Calculation

Details: Calculating the curved surface area is essential in various engineering and architectural applications, particularly in designing domed structures, tanks, and other spherical components where surface area calculations are needed for material estimation and structural analysis.

4. Using the Calculator

Tips: Enter total surface area in square meters, base radius in meters, and top radius in meters. All values must be valid (TSA > 0, radii ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical segment?
A: A spherical segment is the solid portion of a sphere cut off by two parallel planes. It consists of a curved surface and two circular bases.

Q2: How is this different from total surface area?
A: Total surface area includes both the curved surface and the areas of the two circular bases, while curved surface area only includes the lateral curved portion.

Q3: Can the radii be zero?
A: Yes, if one of the cutting planes is tangent to the sphere, the corresponding radius becomes zero, creating a spherical cap.

Q4: What are practical applications of this calculation?
A: This calculation is used in construction (domes, tanks), manufacturing (spherical containers), and various engineering fields where spherical surfaces are involved.

Q5: How accurate is this formula?
A: The formula is mathematically exact and provides precise results when accurate measurements are input.