Spherical Radius of Spherical Sector given Volume Calculator

Formula Used:

\[ r_{Sphere} = \sqrt{\frac{3 \times V}{2 \times \pi \times h_{Cap}}} \]

Spherical Radius (r_Sphere):

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1. What is Spherical Radius of Spherical Sector?

The Spherical Radius of a Spherical Sector is the distance from the center of the sphere to any point on its surface. It is a fundamental measurement that defines the size of the sphere from which the spherical sector is derived.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ r_{Sphere} = \sqrt{\frac{3 \times V}{2 \times \pi \times h_{Cap}}} \]

Where:

\( r_{Sphere} \) — Spherical radius (m)
\( V \) — Volume of spherical sector (m³)
\( h_{Cap} \) — Height of the spherical cap (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the radius of the sphere based on the volume of the spherical sector and the height of its cap, using the mathematical constant pi for geometric calculations.

3. Importance of Spherical Radius Calculation

Details: Calculating the spherical radius is essential in geometry, physics, and engineering applications where spherical sectors are involved. It helps in determining the original sphere's dimensions from which the sector was derived.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical sector?
A: A spherical sector is a portion of a sphere bounded by a conical surface with its vertex at the center of the sphere and the spherical cap it intersects.

Q2: How is this different from sphere radius?
A: The spherical radius refers to the radius of the original sphere from which the spherical sector is cut, not the radius of the sector itself.

Q3: What units should I use?
A: Use consistent units (preferably meters for length and cubic meters for volume) to ensure accurate results.

Q4: Can this formula be used for any spherical sector?
A: Yes, this formula applies to all spherical sectors as long as you have accurate measurements of volume and cap height.

Q5: What if I get an error in calculation?
A: Ensure both input values are positive numbers and the cap height is not zero, as division by zero is mathematically undefined.