Total Surface Area Of Spherical Segment Given Center To Base And Top To Top Radius Length Calculator

Formula Used:

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

Center to Base Radius Length (l_Center-Base):

Height (h):

Top to Top Radius Length (l_Top-Top):

Base Radius (r_Base):

Top Radius (r_Top):

Total Surface Area (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 both the curved surface area and the areas of the two circular bases.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( TSA \) — Total Surface Area of Spherical Segment (m²)
\( l_{Center-Base} \) — Center to Base Radius Length (m)
\( h \) — Height of Spherical Segment (m)
\( l_{Top-Top} \) — Top to Top Radius Length (m)
\( r_{Base} \) — Base Radius of Spherical Segment (m)
\( r_{Top} \) — Top Radius of Spherical Segment (m)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the total surface area by considering the curved surface area and the areas of both circular bases of the spherical segment.

3. Importance of TSA Calculation

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

4. Using the Calculator

Tips: Enter all measurements in meters. All values must be positive numbers greater than zero. The calculator provides results in square meters.

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 between two parallel planes, plus the areas of the two circular bases.

Q3: What are the units for the result?
A: The result is in square meters (m²) since all inputs are in meters.

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

Q5: What if I have measurements in different units?
A: Convert all measurements to meters before entering them into the calculator for accurate results.