Total Surface Area Of Spherical Sector Given Spherical Cap Radius Calculator

Formula Used:

\[ TSA = \frac{\pi}{2} \times \left( \frac{r_{Cap}^2}{h_{Cap}} + h_{Cap} \right) \times \left( (2 \times h_{Cap}) + r_{Cap} \right) \]

Total Surface Area of Spherical Sector:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Total Surface Area of Spherical Sector?

The Total Surface Area of a 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:

\[ TSA = \frac{\pi}{2} \times \left( \frac{r_{Cap}^2}{h_{Cap}} + h_{Cap} \right) \times \left( (2 \times h_{Cap}) + r_{Cap} \right) \]

Where:

\( TSA \) — Total Surface Area of Spherical Sector (m²)
\( r_{Cap} \) — Spherical Cap Radius of Spherical Sector (m)
\( h_{Cap} \) — Spherical Cap Height of Spherical Sector (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the total surface area by considering both the curved surface and the base area of the spherical sector, using the cap radius and height as primary inputs.

3. Importance of Total Surface Area Calculation

Details: Calculating the total surface area of a spherical sector is important in various engineering, architectural, and mathematical applications where precise surface measurements are required for material estimation, structural analysis, or geometric studies.

4. Using the Calculator

Tips: Enter the spherical cap radius and spherical cap height in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: The calculator expects inputs in meters, and the result will be in square meters (m²). You can convert from other units before entering values.

Q2: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for both radius and height inputs for precise calculations.

Q3: What is the difference between spherical cap and spherical sector?
A: A spherical cap is the region of a sphere cut off by a plane, while a spherical sector is the solid generated by rotating a sector of a circle about an axis that passes through the center of the sphere.

Q4: Are there any limitations to this formula?
A: This formula is specifically designed for spherical sectors and assumes perfect spherical geometry. It may not be accurate for irregular or non-spherical shapes.

Q5: Can I use this for practical applications?
A: Yes, this calculator provides accurate results suitable for academic, engineering, and architectural applications involving spherical geometry calculations.