Total Surface Area of Spherical Segment Calculator

Formula Used:

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

Radius of Spherical Segment (r):

Height of Spherical Segment (h):

Base Radius of Spherical Segment (r_Base):

Top Radius of Spherical Segment (r_Top):

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. It includes the curved surface area plus the areas of the top and bottom circular bases.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( TSA \) — Total Surface Area of Spherical Segment (m²)
\( r \) — Radius of Spherical Segment (m)
\( h \) — Height of Spherical Segment (m)
\( r_{Base} \) — 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 summing the areas of the curved surface and the two circular bases of the spherical segment.

3. Importance of TSA Calculation

Details: Calculating the total surface area is crucial for various engineering and architectural applications, material estimation, heat transfer calculations, and surface coating requirements for spherical segments.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive numbers. The calculator provides results in square meters (m²).

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 has two circular bases and a curved surface.

Q2: How does this differ from surface area of a sphere?
A: The total surface area of a spherical segment includes only the portion of the sphere's surface between two parallel cuts, plus the areas of the two circular bases.

Q3: What units should I use for input?
A: The calculator accepts meters as input units, but you can use any consistent unit system as long as all dimensions are in the same units.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q5: What if my spherical segment has only one base?
A: This formula is specifically for spherical segments with two bases. For spherical caps (one base), a different formula should be used.