Radius Of Spherical Segment Given Curved Surface Area Calculator

Formula Used:

\[ r = \frac{CSA}{2 \pi h} \]

Radius of Spherical Segment:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Radius of Spherical Segment?

The radius of a spherical segment is the distance from the center of the sphere to any point on the circumference of the base of the spherical segment. It's a fundamental measurement in spherical geometry.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{CSA}{2 \pi h} \]

Where:

\( r \) — Radius of Spherical Segment (m)
\( CSA \) — Curved Surface Area of Spherical Segment (m²)
\( h \) — Height of Spherical Segment (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the radius of a sphere from which a spherical segment is cut, using the curved surface area and height of the segment.

3. Importance of Radius Calculation

Details: Calculating the radius of a spherical segment is essential in various fields including architecture, engineering, and physics where spherical geometries are involved. It helps in determining the original sphere's dimensions from a given segment.

4. Using the Calculator

Tips: Enter the curved surface area in square meters and the height in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical segment?
A: A spherical segment is the solid portion of a sphere that is cut off by a plane. It's bounded by the cutting plane and the spherical surface.

Q2: How is curved surface area different from total surface area?
A: Curved surface area includes only the spherical surface, while total surface area includes both the curved surface and the base areas of the segment.

Q3: Can this formula be used for any spherical segment?
A: Yes, this formula applies to all spherical segments where the curved surface area and height are known.

Q4: What are practical applications of this calculation?
A: This calculation is used in designing domed structures, calculating volumes of spherical tanks, and in various engineering applications involving spherical geometries.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input values are accurate and the segment follows perfect spherical geometry.