Volume Of Spherical Segment Calculator

Volume Of Spherical Segment Formula:

\[ V = \frac{1}{2} \times \pi \times h \times (r_{Top}^2 + r_{Base}^2 + \frac{h^2}{3}) \]

Height Of Spherical Segment:

Top Radius Of Spherical Segment:

Base Radius Of Spherical Segment:

Volume Of Spherical Segment:

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1. What Is The Volume Of Spherical Segment?

A spherical segment is the solid defined by cutting a sphere with two 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 spherical segment volume formula:

\[ V = \frac{1}{2} \times \pi \times h \times (r_{Top}^2 + r_{Base}^2 + \frac{h^2}{3}) \]

Where:

\( V \) — Volume of spherical segment (m³)
\( \pi \) — Mathematical constant pi (approximately 3.14159)
\( h \) — Height of spherical segment (m)
\( r_{Top} \) — Top radius of spherical segment (m)
\( r_{Base} \) — Base radius of spherical segment (m)

Explanation: This formula calculates the volume of the portion of a sphere between two parallel planes, taking into account the heights and radii of both circular surfaces.

3. Importance Of Volume Calculation

Details: Calculating the volume of spherical segments is important in various engineering, architectural, and manufacturing applications where spherical components or sections are used, such as in tank design, dome construction, and mechanical parts.

4. Using The Calculator

Tips: Enter the height and both radii in meters. All values must be positive numbers. The calculator will compute the volume in cubic meters.

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 does this differ from a spherical cap?
A: A spherical cap is a special case of a spherical segment where one of the radii is zero (the sphere is cut by a single plane).

Q3: What are the units for the result?
A: The volume is calculated in cubic meters (m³) if the input dimensions are in meters. You can convert to other units as needed.

Q4: Can the top and base radii be equal?
A: Yes, when both radii are equal, the spherical segment becomes a spherical zone with parallel circular bases of equal size.

Q5: What if one radius is zero?
A: If one radius is zero, the formula simplifies to that of a spherical cap, which is a valid special case of a spherical segment.