Spherical Radius of Spherical Ring Calculator

Formula Used:

\[ r_{Sphere} = \sqrt{r_{Cylinder}^2 + \frac{h_{Cylinder}^2}{4}} \]

Spherical Radius of Spherical Ring:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Spherical Radius of Spherical Ring?

The Spherical Radius of Spherical Ring is defined as the distance between the centre and any point on the surface of the sphere from which the Spherical Ring is formed. It is a fundamental geometric parameter in three-dimensional geometry.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ r_{Sphere} = \sqrt{r_{Cylinder}^2 + \frac{h_{Cylinder}^2}{4}} \]

Where:

\( r_{Sphere} \) — Spherical Radius of Spherical Ring (m)
\( r_{Cylinder} \) — Cylindrical Radius of Spherical Ring (m)
\( h_{Cylinder} \) — Cylindrical Height of Spherical Ring (m)

Explanation: This formula calculates the spherical radius using the Pythagorean theorem, where the cylindrical radius and half the cylindrical height form the legs of a right triangle, and the spherical radius is the hypotenuse.

3. Importance of Spherical Radius Calculation

Details: Calculating the spherical radius is essential for determining the original sphere's dimensions from which a spherical ring was formed. This has applications in engineering, architecture, and geometric modeling.

4. Using the Calculator

Tips: Enter the cylindrical radius and cylindrical 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 ring?
A: A spherical ring is a three-dimensional geometric shape formed by removing a cylindrical section from a sphere, creating a ring-like structure with spherical outer surfaces.

Q2: How is the cylindrical radius related to the spherical ring?
A: The cylindrical radius is the distance from the center to the circumference of the circular faces of the cylindrical hole in the spherical ring.

Q3: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but the formula works with any consistent unit system as long as both inputs use the same units.

Q4: Can this formula be used for any spherical ring?
A: Yes, this formula applies to all spherical rings where the cylindrical hole is centered within the sphere and perpendicular to the sphere's diameter.

Q5: What if my cylindrical height is zero?
A: If the cylindrical height is zero, the spherical ring degenerates into a sphere, and the spherical radius equals the cylindrical radius.