Total Surface Area of Spherical Sector Calculator

Formula Used:

\[ TSA = \pi \times r_{Sphere} \times ((2 \times h_{Cap}) + r_{Cap}) \]

Spherical Radius of Spherical Sector:

Spherical Cap Height of Spherical Sector:

Spherical Cap Radius of Spherical Sector:

Total Surface Area of Spherical Sector:

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1. What is the Total Surface Area of Spherical Sector?

The 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. It includes both the curved surface area and the base area of the spherical cap.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \pi \times r_{Sphere} \times ((2 \times h_{Cap}) + r_{Cap}) \]

Where:

\( \pi \) — Archimedes' constant (approximately 3.14159)
\( r_{Sphere} \) — Spherical Radius of Spherical Sector (m)
\( h_{Cap} \) — Spherical Cap Height of Spherical Sector (m)
\( r_{Cap} \) — Spherical Cap Radius of Spherical Sector (m)

Explanation: This formula calculates the total surface area by considering both the height and radius of the spherical cap along with the radius of the sphere.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area of a spherical sector is important in various fields including geometry, architecture, engineering, and physics where precise surface measurements are required for material estimation, structural analysis, and design optimization.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure all values are positive numbers. The spherical radius, cap height, and cap radius must all be greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: The calculator uses meters as the default unit. Ensure all measurements are in consistent units for accurate results.

Q2: Can I use this calculator for partial spherical sectors?
A: Yes, this formula works for complete spherical sectors as well as partial ones, as long as you have the correct measurements.

Q3: How accurate is the calculation?
A: The calculation uses the mathematical constant π with high precision, providing results accurate to 6 decimal places.

Q4: What if my spherical cap height is zero?
A: The spherical cap height must be greater than zero. A height of zero would indicate a flat surface, not a spherical sector.

Q5: Can this formula be used for hemispheres?
A: Yes, for a hemisphere, the spherical cap height would equal the spherical radius, and the cap radius would also equal the spherical radius.