Volume Of Spherical Segment Given Total Surface Area And Radius Calculator

Formula Used:

\[ V = \frac{TSA - \pi(r_{Base}^2 + r_{Top}^2)}{12r} \times \left(3r_{Top}^2 + 3r_{Base}^2 + \left(\frac{TSA - \pi(r_{Base}^2 + r_{Top}^2)}{2\pi r}\right)^2\right) \]

Total Surface Area of Spherical Segment (TSA):

m²

Base Radius of Spherical Segment:

Top Radius of Spherical Segment:

Radius of Spherical Segment:

Volume of Spherical Segment:

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1. What is Volume of Spherical Segment?

A spherical segment is the solid defined by cutting a sphere with a pair of parallel planes. The volume of a spherical segment represents the amount of three-dimensional space enclosed within this portion of the sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \frac{TSA - \pi(r_{Base}^2 + r_{Top}^2)}{12r} \times \left(3r_{Top}^2 + 3r_{Base}^2 + \left(\frac{TSA - \pi(r_{Base}^2 + r_{Top}^2)}{2\pi r}\right)^2\right) \]

Where:

\( V \) — Volume of Spherical Segment (m³)
\( TSA \) — Total Surface Area of Spherical Segment (m²)
\( r_{Base} \) — Base Radius of Spherical Segment (m)
\( r_{Top} \) — Top Radius of Spherical Segment (m)
\( r \) — Radius of Spherical Segment (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the volume of a spherical segment using the total surface area and the radii of the segment's boundaries.

3. Importance of Volume Calculation

Details: Calculating the volume of spherical segments is crucial in various engineering, architectural, and scientific applications where spherical geometries are involved, such as in tank design, architectural domes, and geometric modeling.

4. Using the Calculator

Tips: Enter all values in meters and square meters. Ensure all values are positive and the radii are valid for the given spherical segment configuration.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical segment?
A: A spherical segment is the portion of a sphere cut off by two parallel planes. It has two circular bases and a curved surface.

Q2: How is this different from a spherical cap?
A: A spherical cap is a special case of a spherical segment where one of the bases has zero radius (the cutting plane passes through the center of the sphere).

Q3: What are the units for the calculated volume?
A: The volume is calculated in cubic meters (m³) when inputs are in meters and square meters.

Q4: Can this formula handle cases where the segment includes the sphere's center?
A: Yes, the formula works for any spherical segment defined by two parallel cutting planes, regardless of their position relative to the sphere's center.

Q5: What if the top and base radii are equal?
A: If both radii are equal and non-zero, you have a spherical zone (the portion between two parallel planes that don't include the center).