Surface Area Of Hollow Sphere Given Volume And Inner Radius Calculator

Surface Area of Hollow Sphere Formula:

\[ SA = 4\pi\left(\left(\frac{3V}{4\pi} + r_{inner}^3\right)^{\frac{2}{3}} + r_{inner}^2\right) \]

Surface Area of Hollow Sphere (SA):

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1. What is the Surface Area of Hollow Sphere Formula?

The Surface Area of Hollow Sphere formula calculates the total surface area of a hollow sphere given its volume and inner radius. This formula is derived from the relationship between volume and surface area of spherical objects.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA = 4\pi\left(\left(\frac{3V}{4\pi} + r_{inner}^3\right)^{\frac{2}{3}} + r_{inner}^2\right) \]

Where:

\( SA \) — Surface Area of Hollow Sphere (m²)
\( V \) — Volume of Hollow Sphere (m³)
\( r_{inner} \) — Inner Radius of Hollow Sphere (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula calculates the surface area by first determining the outer radius from the given volume and inner radius, then applying the standard surface area formula for a hollow sphere.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of hollow spheres is important in various engineering and manufacturing applications, including material estimation, heat transfer calculations, and structural design.

4. Using the Calculator

Tips: Enter the volume in cubic meters (m³) and inner radius in meters (m). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow sphere?
A: A hollow sphere is a three-dimensional object with a spherical outer surface and a spherical inner cavity, creating a uniform thickness throughout.

Q2: How is this formula derived?
A: The formula is derived by expressing the outer radius in terms of volume and inner radius, then substituting into the standard surface area formula for a hollow sphere.

Q3: What are typical applications of hollow spheres?
A: Hollow spheres are used in various applications including pressure vessels, architectural structures, sports equipment, and scientific instruments.

Q4: Can this calculator handle different units?
A: The calculator requires inputs in meters and cubic meters. For other units, convert to these standard SI units before calculation.

Q5: What is the thickness of the hollow sphere in this calculation?
A: The thickness can be calculated as the difference between the outer and inner radii, which can be derived from the volume and inner radius.